case study questions conic sections class 11

• Class 11 Maths
• Chapter 11: Conic Sections

Important Questions for Class 11 Maths Chapter 11 - Conic Sections

Important questions for class 11 Maths Chapter 11 – conic sections with solutions are given here. The important questions given here are based on the latest exam pattern and previous year question papers and sample papers. Solving these questions will help the students to score good marks in the annual examinations. The case study questions are framed as per the CBSE board syllabus (2022-2023)  and NCERT curriculum . Also, HOTS and value-based questions are asked related to the concept.

Get the Chapter-wise important questions for Class 11 Maths at BYJU’S.

Class 11 Maths Chapter 11 – conic sections will incorporate the concept of sections of cone such as

Learn about these conic sections by solving the questions here. At the end of the article, we have also provided extra questions for chapter 11 conic sections, so that students can practice more on the topic.

Class 11 Chapter 11 – Conic Sections Important Questions with Solutions

To score the good marks in the final examination, practice the problems provided here, which will help you to solve the problems in the annual examination.

Question 1:

Determine the equation of the circle with radius 4 and Centre (-2, 3).

Given that:

Radius, r = 4, and center (h, k) = (-2, 3).

We know that the equation of a circle with centre (h, k) and radius r is given as

(x – h) 2 + (y – k) 2 = r 2 ….(1)

Now, substitute the radius and center values in (1), we get

Therefore, the equation of the circle is

(x + 2) 2 + (y – 3) 2 = (4) 2

x 2 + 4x + 4 + y 2 – 6y + 9 = 16

Now, simplify the above equation, we get:

x 2 + y 2 + 4x – 6y – 3 = 0

Thus, the equation of a circle with center (-2, 3) and radius 4 is x 2 + y 2 + 4x – 6y – 3 = 0

Question 2:

Compute the centre and radius of the circle 2x 2 + 2y 2 – x = 0

Given that, the circle equation is 2x 2 + 2y 2 – x = 0

This can be written as:

⇒ (2x 2 -x) + y 2 = 0

⇒ 2{[x 2 – (x/2)] +y 2 } = 0

⇒{ x 2 – 2x(¼) + (¼) 2 } +y 2 – (¼) 2 = 0

Now, simplify the above form, we get

⇒(x- (¼)) 2 + (y-0) 2 = (¼) 2

The above equation is of the form (x – h) 2 + (y – k) 2 = r 2

Therefore, by comparing the general form and the equation obtained, we can say

h= ¼ , k = 0, and r = ¼.

Question 3:

Determine the focus coordinates, the axis of the parabola, the equation of the directrix and the latus rectum length for y 2 = -8x

Given that, the parabola equation is y 2 = -8x.

It is noted that the coefficient of x is negative.

Therefore, the parabola opens towards the left.

Now, compare the equation with y 2 = -4ax, we obtain

Thus, the value of a is 2.

Therefore, the coordinates of the focus = (-a, 0) = (-2, 0)

Since the given equation involves y 2 , the axis of the parabola is the x-axis.

Equation of directrix, x= a i.e., x = 2

We know the formula to find the length of a latus rectum

Latus rectum length= 4a

Now, substitute a = 2, we get

Length of latus rectum = 8

Question 4:

Determine the foci coordinates, the vertices, the length of the major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse (x 2 /49) + (y 2 /36) = 1

The given equation is (x 2 /49) + (y 2 /36) = 1

It can be written as (x 2 /7 2 ) + (y 2 /6 2 ) = 1

It is noticed that the denominator of x 2 /49 is greater than the denominator of the y 2 /36

On comparing the equation with (x 2 /a 2 ) + (y 2 /b 2 ) = 1, we will get

a= 7 and b = 6

Therefore, c = √(a 2 – b 2 )

Now, substitute the value of a and b

⇒ √(a 2 – b 2 ) = √(7 2 – 6 2 ) = √(49-36)

Hence, the foci coordinates are ( ± √13, 0)

Eccentricity, e = c/a = √13/ 7

Length of the major axis = 2a = 2(7) = 14

Length of the minor axis = 2b = 2(6) =12

The coordinates of the vertices are ( ± 7, 0)

Latus rectum Length= 2b 2 /a = 2(6) 2 /7 = 2(36)/7 = 72/7

Question 5:

Determine the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), the major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Centre = (0, 0), and major axis that passes through the points (3, 2) and (1, 6).

We know that the equation of the ellipse will be of the form when the centre is at (0, 0) and the major axis is on the y-axis,

(x 2 /b 2 ) + (y 2 /a 2 ) = 1 …. (1)

Here, a is the semi-major axis.

It is given that, the ellipse passes through the points (3, 2) and (1, 6).

Hence, equation (1) becomes

(9/b 2 ) + (4/a 2 ) = 1 …(2)

(1/b 2 ) + (36/a 2 ) = 1 …(3)

Solving equation (2) and (3), we get

b 2 = 10 and a 2 = 40

Therefore, the equation of the ellipse becomes: (x 2 /10) + (y 2 /40) = 1

Question 6:

Determine the equation of the hyperbola which satisfies the given conditions: Foci (0, ±13), the conjugate axis is of length 24.

Given that: Foci (0, ±13), Conjugate axis length = 24

It is noted that the foci are on the y-axis.

Therefore, the equation of the hyperbola is of the form:

(y 2 /a 2 )-(x 2 /b 2 ) = 1 …(1)

Since the foci are (0, ±13), we can get

It is given that, the length of the conjugate axis is 24,

It becomes 2b = 24

And, we know that a 2 + b 2 = c 2

To find a, substitute the value of b and c in the above equation:

a 2 + 12 2 = 13 2

a 2 = 169-144

Now, substitute the value of a and b in equation (1), we get

(y 2 /25)-(x 2 /144) = 1, which is the required equation of the hyperbola.

More Articles for Class 11

• Class 11 Syllabus
• Important 1 Mark Questions for CBSE Class 11 Maths
• Important 4 Marks Questions for CBSE Class 11 Maths
• Important 6 Marks Questions for CBSE Class 11 Maths
• Tips to score better marks in class 11 Maths Exam

Practice Problems for Class 11 Maths Chapter 11 Conic Sections

These class 11 Conic Sections questions are categorized into short answer type questions and long answer type questions. These extra questions cover various concepts which will help class 11 students to develop problem-solving skills for the exam.

• Calculate the equation of a circle that passes through the origin and cuts off intercepts -2 and 3 from the axis and the y-axis respectively. (Solution: x 2 + y 2 + 2x -3y)
• Determine the equation of the circle passing through the points – (0,0)(5,0) and (3,3). (Solution: x 2 + y 2 – 5x -y =0), centre (5/2 , ½) and radius = √ 26/2).
• If the distance between the foci of a hyperbola is 16 and eccentricity is √ 2, then obtain its equation. (Solution: x 2 – y 2 =32)
• If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse. (Solution: (√ 5 – 1) / 2)
• Determine the equation of the ellipse whose foci are (4,0) and (-4,0), eccentricity = ⅓. (Solution: x 2 / 9 + y 2 /8 = 16)
• Write the equation of the parabola whose vertex is at (-3,0) and the directrix is (x + 5 ) = 0. (Solution: y 2 = 8(x + 3))
• AB is a double ordinate of a parabola y 2 = 4px. Find the locus of its points of trisection. (Solution: 9y 2 =4px)
• Calculate the equation of the parabola whose focus is (1, -1) and whose vertex is (2,1). Also, find its axis and latus- rectum). (Solution: 4 √ 5).
• Find the equation of the circle which circumscribes the triangle formed by the lines x = 0, y = 0 and lx +my = 1. (Solution: x 2 + y 2 – (1/l)x – (1/m)y = 0)
• Prove that the points (9,1) ( 7,9) (-2, 12) and (6,10) are concyclic.
• Find the equation of ellipse whose eccentricity is 2/3, latus rectum is 5 and the centre is (0,0).
• Find the equation of the circle which touches x-axis and whose centre is (1,2).
• Find the coordinates of a point on the parabola y 2 =8x whose focal distance is 4.

For more solved and important problems in Class 11 Maths concepts, register with BYJU’S – The Learning App and download the app today!

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

myCBSEguide

• Mathematics
• Class 11 Mathematics Case...

Class 11 Mathematics Case Study Questions

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

If you’re seeking a comprehensive and dependable study resource with Class 11 mathematics case study questions for CBSE, myCBSEguide is the place to be. It has a wide range of study notes, case study questions, previous year question papers, and practice questions to help you ace your examinations. Furthermore, it is routinely updated to bring you up to speed with the newest CBSE syllabus. So, why delay? Begin your path to success with myCBSEguide now!

The rationale behind teaching Mathematics

The general rationale to teach Mathematics at the senior secondary level is to assist students:

• In knowledge acquisition and cognitive understanding of basic ideas, words, principles, symbols, and mastery of underlying processes and abilities, notably through motivation and visualization.
• To experience the flow of arguments while demonstrating a point or addressing an issue.
• To use the information and skills gained to address issues using several methods wherever possible.
• To cultivate a good mentality in order to think, evaluate, and explain coherently.
• To spark interest in the subject by taking part in relevant tournaments.
• To familiarise pupils with many areas of mathematics utilized in daily life.
• To pique students’ interest in studying mathematics as a discipline.

Case studies in Class 11 Mathematics

A case study in mathematics is a comprehensive examination of a specific mathematical topic or scenario. Case studies are frequently used to investigate the link between theory and practise, as well as the connections between different fields of mathematics. A case study will frequently focus on a specific topic or circumstance and will investigate it using a range of methodologies. These approaches may incorporate algebraic, geometric, and/or statistical analysis.

Sample Class 11 Mathematics case study questions

When it comes to preparing for Class 11 Mathematics, one of the best things Class 11 Mathematics students can do is to look at some Class 11 Mathematics sample case study questions. Class 11 Mathematics sample case study questions will give you a good idea of the types of Class 11 Mathematics sample case study questions that will be asked in the exam and help you to prepare more effectively.

Looking at sample questions is also a good way to identify any areas of weakness in your knowledge. If you find that you struggle with a particular topic, you can then focus your revision on that area.

myCBSEguide offers ample Class 11 Mathematics case study questions, so there is no excuse. With a little bit of preparation, Class 11 Mathematics students can boost their chances of getting the grade they deserve.

Some samples of Class 11 Mathematics case study questions are as follows:

Class 11 Mathematics case study question 1

• 9 km and 13 km
• 9.8 km and 13.8 km
• 9.5 km and 13.5 km
• 10 km and 14 km
• x  ≤   −1913
• x <  −1613
• −1613  < x <  −1913
• There are no solution.
• y  ≤   12 x+2
• y >  12 x+2
• y  ≥   12 x+2
• y <  12 x+2

Answer Key:

• (b) 9.8 km and 13.8 km
• (a) −1913   ≤  x 
• (b)  y >  12 x+2
• (d) (-5, 5)

Class 11 Mathematics case study question 2

• 2 C 1 × 13 C 10
• 2 C 1 × 10 C 13
• 1 C 2 × 13 C 10
• 2 C 10 × 13 C 10
• 6 C 2​ × 3 C 4   × 11 C 5 ​
• 6 C 2​ × 3 C 4   × 11 C 5
• 6 C 2​ × 3 C 5 × 11 C 4 ​
• 6 C 2 ​  ×   3 C 1 ​  × 11 C 5 ​
• (b) (13) 4  ways
• (c) 2860 ways.

Class 11 Mathematics case study question 3

Read the Case study given below and attempt any 4 sub parts: Father of Ashok is a builder, He planned a 12 story building in Gurgaon sector 5. For this, he bought a plot of 500 square yards at the rate of Rs 1000 /yard². The builder planned ground floor of 5 m height, first floor of 4.75 m and so on each floor is 0.25 m less than its previous floor.

Class 11 Mathematics case study question 4

Read the Case study given below and attempt any 4 sub parts: villages of Shanu and Arun’s are 50km apart and are situated on Delhi Agra highway as shown in the following picture. Another highway YY’ crosses Agra Delhi highway at O(0,0). A small local road PQ crosses both the highways at pints A and B such that OA=10 km and OB =12 km. Also, the villages of Barun and Jeetu are on the smaller high way YY’. Barun’s village B is 12km from O and that of Jeetu is 15 km from O.

Now answer the following questions:

• 5x + 6y = 60
• 6x + 5y = 60
• (a) (10, 0)
• (b) 6x + 5y = 60
• (b) 60/√ 61 km
• (d) 2√61 km

A peek at the Class 11 Mathematics curriculum

The Mathematics Syllabus has evolved over time in response to the subject’s expansion and developing societal requirements. The Senior Secondary stage serves as a springboard for students to pursue higher academic education in Mathematics or professional subjects such as Engineering, Physical and Biological Science, Commerce, or Computer Applications. The current updated curriculum has been prepared in compliance with the National Curriculum Framework 2005 and the instructions provided by the Focus Group on Teaching Mathematics 2005 in order to satisfy the rising demands of all student groups. Greater focus has been placed on the application of various principles by motivating the themes from real-life events and other subject areas.

Class 11 Mathematics (Code No. 041)

Design of Class 11 Mathematics exam paper

CBSE Class 11 mathematics question paper is designed to assess students’ understanding of the subject’s essential concepts. Class 11 mathematics question paper will assess their problem-solving and analytical abilities. Before beginning their test preparations, students in Class 11 maths should properly review the question paper format. This will assist Class 11 mathematics students in better understanding the paper and achieving optimum scores. Refer to the Class 11 Mathematics question paper design provided.

 Class 11 Mathematics Question Paper Design

• No chapter-wise weightage. Care to be taken to cover all the chapters.
• Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.  

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections.

  Prescribed Books:

• Mathematics Textbook for Class XI, NCERT Publications
• Mathematics Exemplar Problem for Class XI, Published by NCERT
• Mathematics Lab Manual class XI, published by NCERT

myCBSEguide guarantees LHS=RHS

With myCBSEguide it will always be LHS=RHS, Hence Proved!

myCBSEguide is a prominent streaming resource for students studying for CBSE examinations. The site offers extensive study material, practice papers, case study questions, online examinations, and other resources at the push of a click. myCBSEguide also has a mobile app for learning on the move. There’s no excuse not to try myCBSEguide with so much convenience and simplicity of access! Hence Proved!

Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Related Posts

• Competency Based Learning in CBSE Schools
• Class 11 Physical Education Case Study Questions
• Class 11 Sociology Case Study Questions
• Class 12 Applied Mathematics Case Study Questions
• Class 11 Applied Mathematics Case Study Questions
• Class 11 Biology Case Study Questions
• Class 12 Physical Education Case Study Questions
• Class 12 Computer Science Case Study Questions

1 thought on “Class 11 Mathematics Case Study Questions”

teri meri meri teri prem kahani hai muskil dolabjo main sayana hop jaye ek ladka aur ek ladki ki prem kahani hai muskil

Leave a Comment

Save my name, email, and website in this browser for the next time I comment.

Gurukul of Excellence

Classes for Physics, Chemistry and Mathematics by IITians

Join our Telegram Channel for Free PDF Download

Download Case Study Questions for Class 11 Maths

• Last modified on: 9 months ago
• Reading Time: 9 Minutes

[PDF] Download Case Study Questions for Class 11 Maths

Here we are providing case study questions for Class 11 Maths. In this article, we are sharing links for Class 11 Maths All Chapters. All case study questions of Class 11 Maths are solved so that students can check their solutions after attempting questions.

Click on the chapter to view.

Class 11 Maths Chapters

Chapter 1 Sets Chapter 2 Relations and Functions Chapter 3 Trigonometric Functions Chapter 4 Principle of Mathematical Induction Chapter 5 Complex Numbers and Quadratic Equations Chapter 6 Linear Inequalities Chapter 7 Permutation and Combinations Chapter 8 Binomial Theorem Chapter 9 Sequences and Series Chapter 10 Straight Lines Chapter 11 Conic Sections Chapter 12 Introduction to Three-Dimensional Geometry Chapter 13 Limits and Derivatives Chapter 14 Mathematical Reasoning Chapter 15 Statistics Chapter 16 Probability

What is meant by Case Study Question?

In the context of CBSE (Central Board of Secondary Education), a case study question is a type of question that requires students to analyze a given scenario or situation and apply their knowledge and skills to solve a problem or answer a question related to the case study.

Case study questions typically involve a real-world situation that requires students to identify the problem or issue, analyze the relevant information, and apply their understanding of the relevant concepts to propose a solution or answer a question. These questions may involve multiple steps and require students to think critically, apply their problem-solving skills, and communicate their reasoning effectively.

Importance of Solving Case Study Questions for Class 11 Maths

Case study questions are an important aspect of mathematics education at the Class 11 level. These questions require students to apply their knowledge and skills to real-world scenarios, helping them develop critical thinking, problem-solving, and analytical skills. Here are some reasons why case study questions are important in Class 11 maths education:

• Real-world application: Case study questions allow students to see how the concepts they are learning in mathematics can be applied in real-life situations. This helps students understand the relevance and importance of mathematics in their daily lives.
• Higher-order thinking: Case study questions require students to think critically, analyze data, and make connections between different concepts. This helps develop higher-order thinking skills, which are essential for success in both academics and real-life situations.
• Collaborative learning: Case study questions often require students to work in groups, which promotes collaborative learning and helps students develop communication and teamwork skills.
• Problem-solving skills: Case study questions require students to apply their knowledge and skills to solve complex problems. This helps develop problem-solving skills, which are essential in many careers and in everyday life.
• Exam preparation: Case study questions are included in exams and tests, so practicing them can help students prepare for these assessments.

Overall, case study questions are an important component of Class 11 mathematics education, as they help students develop critical thinking, problem-solving, and analytical skills, which are essential for success in both academics and real-life situations.

Feature of Case Study Questions on This Website

Here are some features of a Class 11 Maths Case Study Questions Booklet:

Many Case Study Questions: This website contains many case study questions, each with a unique scenario and problem statement.

Different types of problems: The booklet includes different types of problems, such as optimization problems, application problems, and interpretation problems, to test students’ understanding of various mathematical concepts and their ability to apply them to real-world situations.

Multiple-choice questions: Questions contains multiple-choice questions to assess students’ knowledge, understanding, and critical thinking skills.

Focus on problem-solving skills: The questions are designed to test students’ problem-solving skills, requiring them to identify the problem, select appropriate mathematical tools, and analyze and interpret the results.

Emphasis on practical applications: The case studies in the booklet focus on practical applications of mathematical concepts, allowing students to develop an understanding of how mathematics is used in real-life situations.

Comprehensive answer key: The booklet includes a comprehensive answer key that provides detailed explanations and step-by-step solutions for all the questions, helping students to understand the concepts and methods used to solve each problem.

Download CBSE Books

Exam Special Series:

• Sample Question Paper for CBSE Class 10 Science (for 2024)
• Sample Question Paper for CBSE Class 10 Maths (for 2024)
• CBSE Most Repeated Questions for Class 10 Science Board Exams
• CBSE Important Diagram Based Questions Class 10 Physics Board Exams
• CBSE Important Numericals Class 10 Physics Board Exams
• CBSE Practical Based Questions for Class 10 Science Board Exams
• CBSE Important “Differentiate Between” Based Questions Class 10 Social Science
• Sample Question Papers for CBSE Class 12 Physics (for 2024)
• Sample Question Papers for CBSE Class 12 Chemistry (for 2024)
• Sample Question Papers for CBSE Class 12 Maths (for 2024)
• Sample Question Papers for CBSE Class 12 Biology (for 2024)
• CBSE Important Diagrams & Graphs Asked in Board Exams Class 12 Physics
• Master Organic Conversions CBSE Class 12 Chemistry Board Exams
• CBSE Important Numericals Class 12 Physics Board Exams
• CBSE Important Definitions Class 12 Physics Board Exams
• CBSE Important Laws & Principles Class 12 Physics Board Exams
• 10 Years CBSE Class 12 Chemistry Previous Year-Wise Solved Papers (2023-2024)
• 10 Years CBSE Class 12 Physics Previous Year-Wise Solved Papers (2023-2024)
• 10 Years CBSE Class 12 Maths Previous Year-Wise Solved Papers (2023-2024)
• 10 Years CBSE Class 12 Biology Previous Year-Wise Solved Papers (2023-2024)
• ICSE Important Numericals Class 10 Physics BOARD Exams (215 Numericals)
• ICSE Important Figure Based Questions Class 10 Physics BOARD Exams (230 Questions)
• ICSE Mole Concept and Stoichiometry Numericals Class 10 Chemistry (65 Numericals)
• ICSE Reasoning Based Questions Class 10 Chemistry BOARD Exams (150 Qs)
• ICSE Important Functions and Locations Based Questions Class 10 Biology
• ICSE Reasoning Based Questions Class 10 Biology BOARD Exams (100 Qs)

✨ Join our Online JEE Test Series for 499/- Only (Web + App) for 1 Year

✨ Join our Online NEET Test Series for 499/- Only for 1 Year

Leave a Reply Cancel reply

Join our Online Test Series for CBSE, ICSE, JEE, NEET and Other Exams

Editable Study Materials for Your Institute - CBSE, ICSE, State Boards (Maharashtra & Karnataka), JEE, NEET, FOUNDATION, OLYMPIADS, PPTs

Discover more from Gurukul of Excellence

Subscribe now to keep reading and get access to the full archive.

Type your email…

Continue reading

CBSE Question Bank for Class 11 Maths Chapter 11 Conic Sections Free PDF

LEVEL UP CBSE Question Bank for Class 11 Maths Chapter 11 Conic Sections  will provide you with  detailed, latest, comprehensive  &  confidence inspiring   solutions  to the maximum number of Questions covering all the  topics from  your  NCERT Text Books !

Given below are the  Important Questions for Class 11 Maths  (with Solutions) from the exam point of view. To download the “ CBSE Question Bank for Class 11 Maths”,  just click on the “ Download PDF ” and “ Download Solutions ” buttons

CBSE Question Bank for Class 11 Maths Chapter 11 Conic Sections PDF

Checkout our cbse question banks for other chapters.

• Chapter 9 Sequences and Series CBSE Question Bank
• Chapter 10 Straight Lines CBSE Question Bank
• Chapter 12 Introduction to 3D Geometry CBSE Question Bank
• Chapter 13 Limits and Derivatives CBSE Question Bank

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

Comments are closed.

Contact Form

Privacy Policy

• Class 6 Maths
• Class 6 Science
• Class 6 Social Science
• Class 6 English
• Class 7 Maths
• Class 7 Science
• Class 7 Social Science
• Class 7 English
• Class 8 Maths
• Class 8 Science
• Class 8 Social Science
• Class 8 English
• Class 9 Maths
• Class 9 Science
• Class 9 Social Science
• Class 9 English
• Class 10 Maths
• Class 10 Science
• Class 10 Social Science
• Class 10 English
• Class 11 Maths
• Class 11 Computer Science (Python)
• Class 11 English
• Class 12 Maths
• Class 12 English
• Class 12 Economics
• Class 12 Accountancy
• Class 12 Physics
• Class 12 Chemistry
• Class 12 Biology
• Class 12 Computer Science (Python)
• Class 12 Physical Education
• GST and Accounting Course
• Excel Course
• Tally Course
• Finance and CMA Data Course
• Payroll Course

Interesting

• Learn English
• Learn Excel
• Learn Tally
• Learn GST (Goods and Services Tax)
• Learn Accounting and Finance
• GST Tax Invoice Format
• Accounts Tax Practical
• Tally Ledger List
• GSTR 2A - JSON to Excel

Are you in school ? Do you love Teachoo?

We would love to talk to you! Please fill this form so that we can contact you

You are learning...

Chapter 10 Class 11 Conic Sections

Click on any of the links below to start learning from Teachoo ...

Updated for new NCERT Book - 2023-24 .

Learn Chapter 10 Conic Sections of Class 11 free with solutions of all NCERT Questions, Examples and Miscellaneous exercises. All solutions are provided with step-by-step explanation for your reference.

Let's see what conic section is.

We learned Straight Lines in the last chapter, but straight lines are not the only type of curves we have.

In this chapter, we talk about Conic Sections,

that is, sections of the cone

Specifically, we talk about 

Circles, Ellipse, Parabola and Hyperbola

So, the topics of the chapter include

• Circles - How to find equation of circle, center of circle
• Parabola - Equation of parabola, its directrix, eccentricity and focus
• Ellipse - Equation of ellipse, its directrix, eccentricity, focus and vertices
• Hyperbola - Equation of hyperbola, its directrix, eccentricity, focus and vertices
• Other questions like mirror problem , Triangle in parabola problem, Beam problem, Locus, Path traced problems

Click on an exercise to start with answers of the questions, or the topic to learn the concepts with the questions

Serial order wise

Concept wise.

What's in it?

Hi, it looks like you're using AdBlock :(

Please login to view more pages. it's free :), solve all your doubts with teachoo black.

CBSE Class 11 Maths – Chapter 11 Conic Sections- Study Materials

NCERT Solutions Class 11 All Subjects Sample Papers Past Years Papers

Conic Sections : Notes and Study Materials -pdf

• Concepts of  Conic Sections
• Conic Sections Master File
• R D Sharma Solution of Parabola
• R D Sharma Solution of Hyperbola
• R D Sharma Solution of Ellipse
• R D Sharma Solution of Circle
• NCERT Solution  Conic Sections
• NCERT  Exemplar Solution Conic Sections
• Conic Sections : Solved Example 1

CBSE Class 11 Maths Notes Chapter 11 Conic Sections

Circle A circle is the set of all points in a plane, which are at a fixed distance from a fixed point in the plane. The fixed point is called the centre of the circle and the distance from centre to any point on the circle is called the radius of the circle. The equation of a circle with radius r having centre (h, k) is given by (x – h) 2  + (y – k) 2  = r 2 .

The general equation of the circle is given by x 2  + y 2  + 2gx + 2fy + c = 0 , where, g, f and c are constants.

• The centre of the circle is (-g, -f).
• The radius of the circle is r =  g 2 + f 2 − c −−−−−−−−−√

The general equation of the circle passing through origin is x 2  + y 2  + 2gx + 2fy = 0.

The parametric equation of the circle x 2  + y 2  = r 2  are given by x = r cos θ, y = r sin θ, where θ is the parametre and the parametric equation of the circle (x – h) 2  + (y – k) 2  = r 2  are given by x = h + r cos θ, y = k + r sin θ.

Note: The general equation of the circle involves three constants which implies that at least three conditions are required to determine a circle uniquely.

Parabola A parabola is the set of points P whose distances from a fixed point F in the plane are equal to their distance from a fixed line l in the plane. The fixed point F is called focus and the fixed line l is the directrix of the parabola.

Main Facts About the Parabola

Conic Sections Class 11 MCQs Questions with Answers

Question 1. The locus of the point from which the tangent to the circles x² + y² – 4 = 0 and x² + y² – 8x + 15 = 0 are equal is given by the equation (a) 8x + 19 = 0 (b) 8x – 19 = 0 (c) 4x – 19 = 0 (d) 4x + 19 = 0

Answer: (b) 8x – 19 = 0 Hint: Given equation of circles are x² + y² – 4 = 0 and x² + y² – 8x + 15 = 0 Now, the required line is the radical axis of the two circles are (x² + y² – 4) – (x² + y² – 8x + 15) = 0 ⇒ x² + y² – 4 – x² – y² + 8x – 15 = 0 ⇒ 8x – 19 = 0

Question 2. The perpendicular distance from the point (3, -4) to the line 3x – 4y + 10 = 0 (a) 7 (b) 8 (c) 9 (d) 10

Answer: (a) 7 Hint: The perpendicular distance = {3 × 3 – 4 × (-4) + 10}/√(3² + 4²) = {9 + 16 + 10}/√(9 + 16) = 35/√25 = 35/5 = 7

Question 3. A man running a race course notes that the sum of the distances from the two flag posts from him is always 10 meter and the distance between the flag posts is 8 meter. The equation of posts traced by the man is (a) x²/9 + y²/5 = 1 (b) x²/9 + y2 /25 = 1 (c) x²/5 + y²/9 = 1 (d) x²/25 + y²/9 = 1

Question 4. The center of the ellipse (x + y – 2)² /9 + (x – y)² /16 = 1 is (a) (0, 0) (b) (0, 1) (c) (1, 0) (d) (1, 1)

Answer: (d) (1, 1) Hint: The center of the given ellipse is the point of intersection of the lines x + y – 2 = 0 and x – y = 0 After solving, we get x = 1, y = 1 So, the center of the ellipse is (1, 1)

Question 5. The parametric coordinate of any point of the parabola y² = 4ax is (a) (-at², -2at) (b) (-at², 2at) (c) (a sin²t, -2a sin t) (d) (a sin t, -2a sin t)

Answer: (c) (a sin²t, -2a sin t) Hint: The point (a sin²t, -2a sin t) satisfies the equation of the parabola y² = 4ax for all values of t. So, the parametric coordinate of any point of the parabola y² = 4ax is (a sin²t, -2a sin t)

Question 6. The equation of parabola with vertex at origin the axis is along x-axis and passing through the point (2, 3) is (a) y² = 9x (b) y² = 9x/2 (c) y² = 2x (b) y² = 2x/9

Answer: (b) y² = 9x/2 Hint: A parabola with its axis along the x-axis and vertex(0, 0) and direction x = -a has the equation: y² = 4ax ………….. 1 Given, point (2,3) lies on the parabola, ⇒ 3² = 4a × 2 ⇒ 9 = 4a × 2 ⇒ 9/2 = 4a From equation 1, we get y² = (9/2)x ⇒ y² = 9x/2 This is the required equation of the parabola.

Question 7. At what point of the parabola x² = 9y is the abscissa three times that of ordinate (a) (1, 1) (b) (3, 1) (c) (-3, 1) (d) (-3, -3)

Answer: (b) (3, 1) Hint: Given, parabola is x² = 9y Let P(h, k) is the point on the parabola such that abscissa is 3 times the ordinate. So, h = 3k ……… 1 Since P(h, k) lies on the parabola So, h² = 9k ……… 2 From equation 1 and 2, we get (3k)² = 9k ⇒ 9k² = 9k ⇒ 9k² – 9k = 0 ⇒ 9k(k – 1) = 0 ⇒ k = 0, 1 When k = 0, h = 0 So k = 1 Now, from equation 1, h = 3 × 1 = 3 So, the point is (3, 1)

Question 8. The number of tangents that can be drawn from (1, 2) to x² + y² = 5 is (a) 0 (b) 1 (c) 2 (d) More than 2

Answer: (b) 1 Hint: Given point (1, 2) and equation of circle is x² + y² = 5 Now, x² + y² – 5 = 0 Put (1, 2) in this equation, we get 1² + 2² – 5 = 1 + 4 – 5 = 5 – 5 = 0 So, the point (1, 2) lies on the circle. Hence, only one tangent can be drawn.

Question 9. In an ellipse, the distance between its foci is 6 and its minor axis is 8 then its eccentricity is (a) 4/5 (b) 1/√52 (c) 3/5 (d) 1/2

Answer: (c) 3/5 Hint: Given, distance between foci = 6 ⇒ 2ae = 6 ⇒ ae = 3 Again minor axis = 8 ⇒ 2b = 8 ⇒ b = 4 ⇒ b² = 16 ⇒ a² (1 – e²) = 16 ⇒ a² – a² e² = 16 ⇒ a² – (ae)² = 16 ⇒ a² – 3² = 16 ⇒ a² – 9 = 16 ⇒ a² = 9 + 16 ⇒ a² = 25 ⇒ a = 5 Now, ae = 3 ⇒ 5e = 3 ⇒ e = 3/5 So, the eccentricity is 3/5

Question 10. If the length of the tangent from the origin to the circle centered at (2, 3) is 2 then the equation of the circle is (a) (x + 2)² + (y – 3)² = 3² (b) (x – 2)² + (y + 3)² = 3² (c) (x – 2)² + (y – 3)² = 3² (d) (x + 2)² + (y + 3)² = 3²

Answer: (c) (x – 2)² + (y – 3)² = 3² Hint: Radius of the circle = √{(2 – 0)² + (3 – 0)² – 2²} = √(4 + 9 – 4) = √9 = 3 So, the equation of the circle = (x – 2)² + (y – 3)² = 3²

Question 11. The equation of parabola whose focus is (3, 0) and directrix is 3x + 4y = 1 is (a) 16x² – 9y² – 24xy – 144x + 8y + 224 = 0 (b) 16x² + 9y² – 24xy – 144x + 8y – 224 = 0 (c) 16x² + 9y² – 24xy – 144x – 8y + 224 = 0 (d) 16x² + 9y² – 24xy – 144x + 8y + 224 = 0

Answer: (d) 16x² + 9y² – 24xy – 144x + 8y + 224 = 0 Hint: Given focus S(3, 0) and equation of directrix is: 3x + 4y = 1 ⇒ 3x + 4y – 1 = 0 Let P (x, y) be any point on the required parabola and let PM be the length of the perpendicular from P on the directrix Then, SP = PM ⇒ SP² = PM² ⇒ (x – 3)² + (y – 0)² = {(3x + 4y – 1) /{√(3² + 4²)}² ⇒ x² + 9 – 6x + y² = (9x² + 16y² + 1 + 24xy – 8y – 6x)/25 ⇒ 25(x² + 9 – 6x + y²) = 9x² + 16y² + 1 + 24xy – 8y – 6x ⇒ 25x² + 225 – 150x + 25y² = 9x² + 16y² + 1 + 24xy – 8y – 6x ⇒ 25x² + 225 – 150x + 25y² – 9x² – 16y² – 1 – 24xy + 8y + 6x = 0 ⇒ 16x² + 9y² – 24xy – 144x + 8y + 224 = 0 This is the required equation of parabola.

Question 12. The parametric representation (2 + t², 2t + 1) represents (a) a parabola (b) a hyperbola (c) an ellipse (d) a circle

Answer: (a) a parabola Hint: Let x = 2 + t² ⇒ x – 2 = t² ……….. 1 and y = 2t + 1 ⇒ y – 1 = 2t ⇒ (y – 1)/2 = t From equation 1, we get x – 2 = {(y – 1)/2}² ⇒ x – 2 = (y – 1)²/4 ⇒ (y – 1)² = 4(x – 2) This represents the equation of a parabola.

Question 13. The equation of a hyperbola with foci on the x-axis is (a) x²/a² + y²/b² = 1 (b) x²/a² – y²/b² = 1 (c) x² + y² = (a² + b²) (d) x² – y² = (a² + b²)

Answer: (b) x²/a² – y²/b² = 1 Hint: The equation of a hyperbola with foci on the x-axis is defined as x²/a² – y²/b² = 1

Question 14. The equation of parabola with vertex (-2, 1) and focus (-2, 4) is (a) 10y = x² + 4x + 16 (b) 12y = x² + 4x + 16 (c) 12y = x² + 4x (d) 12y = x² + 4x + 8

Answer: (b) 12y = x² + 4x + 16 Hint: Given, parabola having vertex is (-2, 1) and focus is (-2, 4) As the vertex and focus share the same abscissa i.e. -2, parabola axis of symmetry as x = -2 ⇒ x + 2 = 0 Hence, the equation of a parabola is of the type (y – k) = a(x – h)² where (h, k) is vertex Now, focus = (h, k + 1/4a) Since, vertex is (-2, 1) and parabola passes through vertex So, focus = (-2, 1 + 1/4a) Now, 1 + 1/4a = 4 ⇒ 1/4a = 4 -1 ⇒ 1/4a = 3 ⇒ 4a = 1/3 ⇒ a = /1(3 × 4) ⇒ a = 1/12 Now, equation of parabola is (y – 1) = (1/12) × (x + 2)² ⇒ 12(y – 1) = (x + 2)² ⇒ 12y – 12 = x² + 4x + 4 ⇒ 12y = x² + 4x + 4 + 12 ⇒ 12y = x² + 4x + 16 This is the required equation of parabola.

Question 15. If a parabolic reflector is 20 cm in diameter and 5 cm deep then the focus of parabolic reflector is (a) (0 0) (b) (0, 5) (c) (5, 0) (d) (5, 5)

Question 16. The radius of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is? (a) √57/4 (b) √77/4 (c) √77/2 (d) √87/4

Answer: (c) √77/2 Hint: Given, equation fo the of the circle is 4x² + 4y² – 8x + 12y – 25 = 0 ⇒ x² + y² – 8x/4 + 12y/4 – 25/4 = 0 ⇒ x² + y² – 2x + 3y – 25/4 = 0 Now, radius = √{(-2)² + (3)² – (-25/4)} = √{4 + 9 + 25/4} = √{13 + 25/4} = √{(13×4 + 25)/4} = √{(52 + 25)/4} = √{77/4} = √77/2

Question 17. If (a, b) is the mid point of a chord passing through the vertex of the parabola y² = 4x, then (a) a = 2b (b) 2a = b (c) a² = 2b (d) 2a = b²

Answer: (d) 2a = b² Hint: Let P(x, y) be the coordinate of the other end of the chord OP where O(0, 0) Now, (x + 0)/2 = a ⇒ x = 2a and (y + 0)/2 = b ⇒ y = 2b Now, y² = 4x ⇒ (2b)² = 4 × 2a ⇒ 4b² = 8a ⇒ b² = 2a

Question 18. A rod of length 12 CM moves with its and always touching the co-ordinate Axes. Then the equation of the locus of a point P on the road which is 3 cm from the end in contact with the x-axis is (a) x²/81 + y²/9 = 1 (b) x²/9 + y²/81 = 1 (c) x²/169 + y²/9 = 1 (d) x²/9 + y²/169 = 1

Question 19. The line lx + my + n = 0 will touches the parabola y² = 4ax if (a) ln = am² (b) ln = am (c) ln = a² m² (d) ln = a² m

Answer: (a) ln = am² Hint: Given, lx + my + n = 0 ⇒ my = -lx – n ⇒ y = (-l/m)x + (-n/m) This will touches the parabola y² = 4ax if (-n/m) = a/(-l/m) ⇒ (-n/m) = (-am/l) ⇒ n/m = am/l ⇒ ln = am²

Question 20. The center of the circle 4x² + 4y² – 8x + 12y – 25 = 0 is? (a) (2,-3) (b) (-2,3) (c) (-4,6) (d) (4,-6)

Answer: (a) (2,-3) Hint: Given, equation fo the of the circle is 4x² + 4y² – 8x + 12y – 25 = 0 ⇒ x² + y² – 8x/4 + 12y/4 – 25/4 = 0 ⇒ x² + y² – 2x + 3y – 25/4 = 0 Now, center = {-(-2), -3} = (2, -3)

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 10: Conic sections

Introduction to conic sections.

• Intro to conic sections (Opens a modal)

The features of a circle

• Graphing circles from features (Opens a modal)
• Features of a circle from its graph (Opens a modal)
• Graph a circle from its features Get 3 of 4 questions to level up!
• Features of a circle from its graph Get 3 of 4 questions to level up!

Standard equation of a circle

• Features of a circle from its standard equation (Opens a modal)
• Graphing a circle from its standard equation (Opens a modal)
• Writing standard equation of a circle (Opens a modal)
• Features of a circle from its standard equation Get 3 of 4 questions to level up!
• Graph a circle from its standard equation Get 3 of 4 questions to level up!
• Write standard equation of a circle Get 3 of 4 questions to level up!

Expanded equation of a circle

• Features of a circle from its expanded equation (Opens a modal)
• Circle equation review (Opens a modal)
• Features of a circle from its expanded equation Get 3 of 4 questions to level up!
• Graph a circle from its expanded equation Get 3 of 4 questions to level up!

Center and radii of an ellipse

• Intro to ellipses (Opens a modal)
• Ellipse standard equation from graph (Opens a modal)
• Ellipse graph from standard equation (Opens a modal)
• Ellipse features review (Opens a modal)
• Ellipse equation review (Opens a modal)
• Graph & features of ellipses Get 3 of 4 questions to level up!
• Center & radii of ellipses from equation Get 3 of 4 questions to level up!
• Ellipse standard equation & graph Get 3 of 4 questions to level up!

Foci of an ellipse

• Foci of an ellipse from equation (Opens a modal)
• Ellipse foci review (Opens a modal)
• Foci of an ellipse from radii Get 3 of 4 questions to level up!
• Foci of an ellipse from equation Get 3 of 4 questions to level up!
• Equation of an ellipse from features Get 3 of 4 questions to level up!

Focus and directrix of a parabola

• Intro to focus & directrix (Opens a modal)
• Equation of a parabola from focus & directrix (Opens a modal)
• Focus & directrix of a parabola from equation (Opens a modal)
• Parabola focus & directrix review (Opens a modal)
• Equation of a parabola from focus & directrix Get 3 of 4 questions to level up!

Introduction to hyperbolas

• Intro to hyperbolas (Opens a modal)
• Vertices & direction of a hyperbola (Opens a modal)
• Vertices & direction of a hyperbola (example 2) (Opens a modal)
• Graphing hyperbolas (old example) (Opens a modal)
• Vertices & direction of a hyperbola Get 3 of 4 questions to level up!

Hyperbolas not centered at the origin

• Equation of a hyperbola not centered at the origin (Opens a modal)

Identifying conic sections from their equation

• Conic section from expanded equation: circle & parabola (Opens a modal)
• Conic section from expanded equation: ellipse (Opens a modal)
• Conic section from expanded equation: hyperbola (Opens a modal)

• New QB365-SLMS
• NEET Materials
• JEE Materials
• Banking first yr Materials
• TNPSC Materials
• DIPLOMA COURSE Materials
• 5th Standard Materials
• 12th Standard Materials
• 11th Standard Materials
• 10th Standard Materials
• 9th Standard Materials
• 8th Standard Materials
• 7th Standard Materials
• 6th Standard Materials
• 12th Standard CBSE Materials
• 11th Standard CBSE Materials
• 10th Standard CBSE Materials
• 9th Standard CBSE Materials
• 8th Standard CBSE Materials
• 7th Standard CBSE Materials
• 6th Standard CBSE Materials
• Tamilnadu Stateboard
• Scholarship Exams
• Scholarships

CBSE 11th Standard CBSE all question papers, important notes , study materials , Previuous Year questions, Syllabus and exam patterns. Free 11th Standard CBSE all books and syllabus online. Practice Online test for free in QB365 Study Material. Important keywords, Case Study Questions and Solutions. Updates about latest education news and Scholorships in one place.

Latest 11th Standard CBSE Case study Questions Update

Cbse 11th physics motion in a straight line chapter case study questions with answers, cbse 11th physics units and measurements chapter case study questions with answers, cbse 11th chemistry structure of atom chapter case study question with answers, cbse 11th chemistry some basic concept of chemistry chapter case study questions with answers, 11th biology biological classification chapter case study question with answers cbse, 11th biology the living world chapter case study question with answers cbse, 11th standard cbse study materials.

11th Standard CBSE Subjects

Class VI to XII

Tn state board / cbse, 3000+ q&a's per subject, score high marks.

Latest CBSE 11th Standard CBSE Study Material Updates

Study Material

Home > Class 11 Math Important Questions

Conic Sections Class 11 Maths Most Important Questions

In Mathematics, Most Important Questions of Conic Sections Class 11 is important for the students as many questions are framed from this chapter in final examinations. In this chapter, you will understand the concepts like standard equations of parabola, circle, ellipse and hyperbola. Relationship between semi-major axis, semi-minor axis, eccentricity, etc.

PREMIUM EDUCART QUESTIONS

<cta2> Download <cta2>

(Important Questions of this Chapter from our 📕)

In the table given below, we have provided the links to Most Important Questions for Class 11 Maths Conic Sections PDFs for Mathematics Chapter 11. You can download them without having to share any login info.

📈 Trending: 2024-25 CBSE Class 11 Syllabus

📝 Recommended: Important Questions PDFs for Class 11

📚 Don’t Miss: Class 11 2024-25 Question Banks

We hope that you practice the above Conic Sections Class 11 Most Important Questions and achieve your dream marks.

All the best!

Extra 10% Discount

CBSE Class 11 Syllabus

Ncert books for class 11, class 11 important questions.

Buy Latest Books

Teacher's Corner

To Download PDF

Please verify your Whatsapp number first, so you can download this pdf immediately

Please type a valid 10 digit whatsapp number

OTP sent, check your whatsapp

Your OTP is incorrect, Please enter valid OTP

• Mathematics (Standard)
• Mathematics (Basic)
• Social Science
• Computer Application
• Information Technology
• English Core
• Mathematics
• Accountancy
• Business Studies
• Political Science
• Science (Hindi )
• Maths (Hindi)
• Social Science (Hindi )
• Applied Maths
• Physical Education
• English Language
• History & Civics
• 10 Year Solved Papers
• Class 10 Science
• Class 10 Maths
• Class 10 English
• Class 12 Physics
• Class 12 Chemistry
• Class 12 Biology
• Class 12 Maths
• Class 12 English
• Math Standard
• Computer Applications
• Class 12 PCB Combo
• Class 12 PCM Combo
• Entrance Exam
• K-8 Raspberry Solutions
• K-8 Kiwi Solutions