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.
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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.
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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.
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It is necessary for students to enhance their problem-solving 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 problem-solving 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.
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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 easy-to-understand 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.
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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. y2 = 12x
2. x2 = 6y
3. y2 = – 8x
4. x2 = – 16y
5. y2 = 10x
6. x2 = – 9y
Ans.
1.
The given equation of parabola is:
y2 = 12x
Since, coefficient of x is positive. So, comparing it with y2 = 4ax and we get
4a = 12
a = 3
The coordinates of the focus is (3, 0).
Since, this equation has y2, so axis is x-axis.
Equation of directrix is: x = – 3.
Length of latus rectum = 4a
= 4 x 3
= 12
2.
The given equation of parabola is: x2 = 6y
Since, coefficient of y is positive. So, comparing it with x2 = 4ay and we get
4a = 6
a = (3/2)
The coordinates of the focus is (0, 3/2).
Since, this equation has x2, so axis is y-axis.
Equation of directrix is: y = – 3/2.
Length of latus rectum = 4a
= 4 x 3/2
= 6
3.
The given equation of parabola is:
y2 = – 8x
Since, coefficient of x is negative. So, comparing it with y2 = – 4ax and we get
– 4a = – 8
a = 2
The coordinates of the focus is (– 2, 0).
Since, this equation has y2, so axis is x-axis.
Equation of directrix is:
x = 2.
Length of latus rectum = 4a
= 4 x 2
= 8
4.
The given equation of parabola is:
x2 = – 16y
Since, coefficient of y is negative. So, comparing it with x2 = – 4ay and we get
4a = – 16
a = –4
The coordinates of the focus is (0, –4).
Since, this equation has x2, so axis is y-axis.
Equation of directrix is: y = 4.
Length of latus rectum = 4a
= 4 x 4
= 16
5.
The given equation of parabola is:
y2 = 10x
Since, coefficient of x is positive. So, comparing it with y2 = 4ax and we get
4a = 10
a = (5/2)
The coordinates of the focus is (5/2, 0).
Since, this equation has y2, so axis is x-axis.
Equation of directrix is: x = – 5/2.
Length of latus rectum = 4a
= 4 x 5/2
= 10
6.
The given equation of parabola is:
x2 = – 9y
Since, coefficient of y is negative. So, comparing it with x2 = – 4ay and we get
4a = – 9
a = – 9/4
The coordinates of the focus is (0, – 9/4).
Since, this equation has x2, so axis is y-axis.
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 x-axis.
12. Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.
Ans.
7. Since, focus (6, 0) lies on x-axis and directrix
x = – 6 shows that parabola is in the form of
y2 = 4ax where a = 6.
Therefore, the equation of parabola is:
y2 = 4(6)x
y2 = 24 x
8. Since, focus (0,–3) lies on y-axis and directrix
y = 3 shows that parabola is in the form of
x2 = – 4ay where a = 3.
Therefore, the equation of parabola is:
x2 = – 4(3)y
x2 = – 12y
9. Since, vertex is (0, 0) and focus is (3, 0) which lies on x-axis of parabola.
Therefore, the equation of parabola will be in the form of y2 = 4ax.
Therefore,
y2 = 4(3)x
y2 = 12x is the required equation of parabola.
10.
Since, vertex is (0, 0) and focus is (–2, 0) which lies on x-axis of parabola.
Therefore, the equation of parabola will be in the form of y2 = – 4ax.
Therefore,
y2 = – 4(2)x
y2 = – 8x is the required equation of parabola.
11.
Since, parabola is along x-axis. So, its possible equation may be either y2 = 4ax or y2 = – 4ax.
Since, parabola is passing through the point (2, 3), which lies in first quadrant.
So, the equation is of the form y2 = 4ax.
The point (2, 3) lies on y2 = 4ax, then
(3)2 = 4a(2)
9 = 8a
a = 9/8
Therefore, the equation of the parabola is
y2 = 4(9/8)x
= (9/2)x
Or 2y2 = 9x, which is required equation.
12.
Since, parabola is along y-axis. So, its possible equation may be either x2 = 4ay or x2 = – 4ay.
Since, parabola is passing through the point (5, 2),
which lies in first quadrant. So, the equation is of the form x2 = 4ay.
The point (5, 2) lies on x2 = 4ay, then
(5)2 = 4a(2)
25 = 8a
a = 25/8
Therefore, the equation of the parabola is
x2 = 4(25/8)y
= (25/2)y
Or 2x2 = 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 problem-solving 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.
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