NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections (Ex 11.2) Exercise 11.2
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Mathematics is one of the most important subjects in the school curriculum. A strong foundation in Mathematics is helpful in achieving success in careers. Students can learn many subjects in an effective way with the knowledge of Mathematics topics. Mathematical concepts have various applications in a range of fields. Mathematics is used in Construction, Robotics, Surveying, Automotive design, etc. In schools, Mathematics is taught as an essential subject. It is significant for enhancing the mental ability and reasoning skills of the students.
Mathematics helps increase the logical and analytical thinking of students. It is widely used in many other fields like Astronomy, Weather Forecasting, Data Science, etc. Students must practice regularly to build a strong foundation in Mathematics. Basic Mathematical calculations are essential for carrying out daily tasks.
Mathematical concepts can be complicated to learn, but with consistent revision and practice, they can be easily mastered. Students studying in Class 11 are supposed to practice each of the exercises in chapter 11 in order to completely grasp its concepts.
The topic discussed in chapter 11 is Conic Sections. All the concepts of Conic Sections need to be practised on a regular basis. Students are advised to make use of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 to solve exercise 11.2 in an efficient manner. It is necessary to revise the concepts of chapter 11 from time to time in order to prepare well for the Mathematics exam.
National Council of Educational Research and Training (NCERT) is an organization developed by the Ministry of Education for regulating the standard of education in the country. All the textbooks and syllabi of the CBSE Board schools are published by the NCERT.
Students are advised to practice the sample papers and past years’ papers of Mathematics regularly in order to prepare well for the Mathematics exam. Solving past years’ papers and sample papers are beneficial for understanding the paper pattern of Mathematics. It also helps students plan their preparation accordingly. Students belonging to Class 11 can access the past years’ papers and sample papers of Mathematics from Extramarks.
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It is necessary to learn new techniques of revising concepts for the students in order to score higher marks in the exams. Online teaching methods enable students to retain the concepts for a longer time. Students must make use of the study materials available on the Extramarks website and mobile application during their exam preparation. Class 11 is an important step in the students’ careers. It is crucial to score well in the final exams of Class 11. The concepts learned in Class 11 are used frequently in Class 12. It becomes necessary to study well in Class 11. Most of the topics covered in Class 11 are also beneficial for the preparation of various competitive exams like the Joint Entrance Exam (JEE) and NEET. Concepts covered in Class 11 lay down a foundation for the topics of future courses like Engineering, Chartered Accountancy, etc.
Students having difficulty in solving the questions of Exercise 11.2 can make use of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. Class 11 students of the Central Board of Secondary Education (CBSE) must download the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 from the Extramarks website and mobile application. NCERT textbooks are the primary source for learning a subject on the CBSE Board. Students are advised to rely on the NCERT textbook for learning the chapters. Each of the topics should be practised thoroughly for increasing understanding of the chapters. It is necessary to revise the basic concepts of the chapters from time to time. Students of Class 11 can review the basics of Chapter 11 with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2.
Class 11 Maths Chapter 11 Exercise 11.2 is based on the Parabola topic. It is important to understand the equations of Parabola in order to practice the questions based on the topic. There are four equations of Parabola, known as the standard equations of parabolas. Students can solve questions related to the Parabola topic with the assistance of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 can also help students in understanding the Parabola topic.
Students are advised to go through the solved problems given in Chapter 11 before solving the exercises in the chapter. Solved examples are very helpful in improving the understanding of the concepts. Class 11 students may come across difficulties in finding the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. Students can easily access the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 from the Extramarks learning platform in PDF format. All the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are prepared by expert teachers of Mathematics. Students are supposed to make use of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 to get easy solutions to Exercise 11.2 problems.
Extramarks has been helping students perform well in their exams. The Extramarks learning platform has all the useful study resources available for students to utilize during the exam preparations. There are many benefits to utilizing the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. The Extramarks learning platform also provides the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. Each of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are updated regularly according to the change in syllabus.
Students can make use of the live lectures at Extramarks to build their concepts of the subjects. The live lectures can be attended on the Extramarks website and mobile application, both. Students can easily get solutions to their issues and doubts during the interactive live classes of Extramarks. The preparation of nationallevel competitive exams like the Joint Entrance Exam (JEE) and NEET is also possible with Extramarks. Students can access all the relevant study materials from the Extramarks website and mobile application to prepare well for the competitive exams.
The Central Board of Secondary Education (CBSE) is an educational board in India that works under the Ministry of India. The CBSE Board is responsible for conducting and managing the board exams every year in India. The syllabus of the CBSE Board is very compact, and the focus is also on imparting practical knowledge to students. Many of the private and public schools in India follow the CBSE curriculum. Students can learn in English as well as in Hindi under the CBSE Board. The Central Board of Secondary Education analyses and monitors the quality of academic activities on a regular basis. Students of the CBSE Board are able to gain a deeper understanding of the concepts in a gradual and thorough manner.
It is necessary for students to enhance their problemsolving skills in order to solve questions in Mathematics. Practising exercise questions with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 is beneficial for enhancing the problemsolving skills of the students. There are 12 questions in Exercise 11.2. To get detailed solutions to the questions of Exercise 11.2, students can utilize the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. It can be difficult to solve question 4 of Exercise 11.2. Students can easily solve question 4 with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2.
The formulae and concepts related to the questions in Exercise 11.2 can be revised with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. Students belonging to Class 11 can access the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 from the Extramarks website and mobile application. All the topics and subtopics in Chapter 11 are essential. Students must focus on solving the questions related to the topics for an indepth understanding.
Students can also access the revision notes for each chapter of Class 11 Mathematics from Extramarks. The revision notes are helpful in quickly reviewing the important concepts, formulae, definitions, theorems, etc. of the chapters. Students are encouraged to practice more in order to increase their calculation speed as well. Practising with the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 is beneficial for increasing the calculation speed of the students. Students can get an idea of the proper methods of solving questions with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2.
It is crucial for Class 11 students to divide their time efficiently while answering questions in the Mathematics exam. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are helpful in learning effective time management skills for the Mathematics exam. Students facing challenges in solving the questions related to the equations of the Parabola can get help from the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2.
To ensure that all the questions of 11.2 Class 11 Maths are practised well, it is important to refer to the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are beneficial for boosting the confidence of the students for the upcoming exam of Mathematics.
Class 11 students can make use of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 during the preparation of the Mathematics examination. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are very helpful resources in obtaining higher marks in the Mathematics exam. It is important for students to assess their methods of finding solutions in Mathematics from time to time. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 can be utilized by Class 11 students for the purpose of selfassessment. It is advised to keep practising the exercise questions of each chapter in order to perform well in the Mathematics exam. Students can develop a habit of practising questions with the assistance of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2.
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections (Ex 11.2) Exercise 11.2
Students belonging to Class 11 can download the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 from the Extramarks website and mobile application in PDF format. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are available on the Extramarks learning platform and are given in a simple and easytounderstand format.
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Exercise 11.2
Exercise 11.2 Class 11 Maths problems can be difficult to solve for students in Class 11. They are advised to go through the derivations of equations of Parabolas in order to understand them in detail. Revising the derivations is useful in finding solutions to the questions. Students can utilize the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 in order to get detailed solutions to Exercise 11.2 questions.
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Exercise 11.2
Students are advised to practice drawing diagrams in order to solve the exercise questions of Chapter 11 efficiently. They can learn to draw diagrams while solving questions with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are very important study materials that students need to refer to while preparing for the Mathematics exam.
The NCERT Solutions are available for all the students of the Central Board of Secondary Education (CBSE) on Extramarks. Students of Class 12 can easily access the NCERT Solutions Class 12 from the Extramarks learning platform. Class 11 students can make use of the NCERT Solutions Class 11 while preparing for the upcoming exams. All the students of Class 10 must access the NCERT Solutions Class 10 from the Extramarks website and mobile application. Students belonging to Class 9 can download the NCERT Solutions Class 9 for all the exercises of a subject from Extramarks. Class 8 students should refer to the NCERT Solutions Class 8 while solving exercises of Mathematics, English, Hindi, etc. The NCERT Solutions Class 7 are accessible on the Extramarks learning platform in PDF format.
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Q.1 In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
1. y^{2} = 12x
2. x^{2} = 6y
3. y^{2} = – 8x
4. x^{2} = – 16y
5. y^{2} = 10x
6. x^{2} = – 9y
Ans.
1.
The given equation of parabola is:
y^{2 }= 12x
Since, coefficient of x is positive. So, comparing it with y^{2 }= 4ax and we get
4a = 12
a = 3
The coordinates of the focus is (3, 0).
Since, this equation has y^{2}, so axis is xaxis.
Equation of directrix is: x = – 3.
Length of latus rectum = 4a
= 4 x 3
= 12
2.
The given equation of parabola is: x^{2 }= 6y
Since, coefficient of y is positive. So, comparing it with x^{2 }= 4ay and we get
4a = 6
a = (3/2)
The coordinates of the focus is (0, 3/2).
Since, this equation has x^{2}, so axis is yaxis.
Equation of directrix is: y = – 3/2.
Length of latus rectum = 4a
= 4 x 3/2
= 6
3.
The given equation of parabola is:
y^{2 }= – 8x
Since, coefficient of x is negative. So, comparing it with y^{2 }= – 4ax and we get
– 4a = – 8
a = 2
The coordinates of the focus is (– 2, 0).
Since, this equation has y^{2}, so axis is xaxis.
Equation of directrix is:
x = 2.
Length of latus rectum = 4a
= 4 x 2
= 8
4.
The given equation of parabola is:
x^{2 }= – 16y
Since, coefficient of y is negative. So, comparing it with x^{2 }= – 4ay and we get
4a = – 16
a = –4
The coordinates of the focus is (0, –4).
Since, this equation has x^{2}, so axis is yaxis.
Equation of directrix is: y = 4.
Length of latus rectum = 4a
= 4 x 4
= 16
5.
The given equation of parabola is:
y^{2 }= 10x
Since, coefficient of x is positive. So, comparing it with y^{2 }= 4ax and we get
4a = 10
a = (5/2)
The coordinates of the focus is (5/2, 0).
Since, this equation has y^{2}, so axis is xaxis.
Equation of directrix is: x = – 5/2.
Length of latus rectum = 4a
= 4 x 5/2
= 10
6.
The given equation of parabola is:
x^{2 }= – 9y
Since, coefficient of y is negative. So, comparing it with x^{2 }= – 4ay and we get
4a = – 9
a = – 9/4
The coordinates of the focus is (0, – 9/4).
Since, this equation has x^{2}, so axis is yaxis.
Equation of directrix is: y = 9/4.
Length of latus rectum = 4a
= 4 x 9/4
= 9
Q.2 In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the given conditions:
7. Focus (6,0); directrix x = – 6
8. Focus (0,–3); directrix y = 3
9. Vertex (0,0); focus (3,0)
10. Vertex (0,0); focus (–2,0)
11. Vertex (0,0) passing through (2,3) and axis is along xaxis.
12. Vertex (0, 0), passing through (5, 2) and symmetric with respect to yaxis.
Ans.
7. Since, focus (6, 0) lies on xaxis and directrix
x = – 6 shows that parabola is in the form of
y^{2} = 4ax where a = 6.
Therefore, the equation of parabola is:
y^{2} = 4(6)x
y^{2} = 24 x
8. Since, focus (0,–3) lies on yaxis and directrix
y = 3 shows that parabola is in the form of
x^{2} = – 4ay where a = 3.
Therefore, the equation of parabola is:
x^{2} = – 4(3)y
x^{2} = – 12y
9. Since, vertex is (0, 0) and focus is (3, 0) which lies on xaxis of parabola.
Therefore, the equation of parabola will be in the form of y^{2} = 4ax.
Therefore,
y^{2} = 4(3)x
y^{2} = 12x is the required equation of parabola.
10.
Since, vertex is (0, 0) and focus is (–2, 0) which lies on xaxis of parabola.
Therefore, the equation of parabola will be in the form of y^{2} = – 4ax.
Therefore,
y^{2} = – 4(2)x
y^{2} = – 8x is the required equation of parabola.
11.
Since, parabola is along xaxis. So, its possible equation may be either y^{2} = 4ax or y^{2} = – 4ax.
Since, parabola is passing through the point (2, 3), which lies in first quadrant.
So, the equation is of the form y^{2} = 4ax.
The point (2, 3) lies on y^{2} = 4ax, then
(3)^{2} = 4a(2)
9 = 8a
a = 9/8
Therefore, the equation of the parabola is
y^{2} = 4(9/8)x
= (9/2)x
Or 2y^{2 }= 9x, which is required equation.
12.
Since, parabola is along yaxis. So, its possible equation may be either x^{2} = 4ay or x^{2} = – 4ay.
Since, parabola is passing through the point (5, 2),
which lies in first quadrant. So, the equation is of the form x^{2} = 4ay.
The point (5, 2) lies on x^{2} = 4ay, then
(5)^{2} = 4a(2)
25 = 8a
a = 25/8
Therefore, the equation of the parabola is
x^{2} = 4(25/8)y
= (25/2)y
Or 2x^{2 }= 25y, which is required equation.
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FAQs (Frequently Asked Questions)
1. What are the various advantages of referring to the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2?
Students can get detailed solutions to Exercise 11.2 with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are helpful in preparing effectively for the Mathematics exam. Class 11 students can learn better problemsolving strategies with the help of the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2.
2. Where can students of Class 11 get access to the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2?
Students of Class 11 can download the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 from the Extramarks website and mobile application. All the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 are beneficial for motivating students to practice more.
3. What are the other resources available on Extramarks apart from the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2?
The revision notes, past years’ papers, sample papers, etc are available on the Extramarks learning platform. All the study materials are very authentic and trustworthy. Students can improve their understanding of each subject with the help of study materials available on Extramarks.
4. Where can a student access the latest syllabus of Class 11 Mathematics?
Students belonging to Class 11 can easily access the CBSE syllabus of Mathematics from the Extramarks website and mobile application. The syllabus is beneficial for getting an overview of all the topics and subtopics covered in Class 11 Mathematics. Students can prepare a learning schedule with the help of the syllabus.
5. Are the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 available in PDF format?
Class 11 students can download the NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 in a PDF format from the Extramarks website and mobile application. The NCERT Solutions For Class 11 Maths Chapter 11 Exercise 11.2 can also be reviewed in offline mode.