NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

 

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NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections

In the previous Chapter, we have studied different forms of the equations of a line. In this Chapter, we will study some other curves like circles, parabolas, hyperbolas and ellipses.  The names hyperbola and parabola are given by Apollonius. There is a total of 62 questions are given in 4 exercises and 8 questions in a miscellaneous exercise. The NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections are solved and prepared by our maths experts. This is an important chapter for maths students because every year many questions are asked from this topic in CBSE class 11 final exam as well as in the various competitive exams. These NCERT solutions are explained in detail and these solutions help students in the preparation of their class 11 exams and also in competitive exams like JEE Mains, VITEEE, BITSAT etc.

In NCERT Class 11 Maths Chapter 11 Conic Sections, students will get to know about four curves which are circle, parabola, ellipse, and hyperbola. These curves are known as conic sections because these curves are the results of intersections of a plane with the double-napped right circular cone. The applications of these curves are in fields like the design of antennas and telescopes, planetary motion, reflectors in automobile headlights, etc. The NCERT Class 11 Maths Chapter 11 Conic Sections contain four exercises, the first exercise is on the circle, second on the parabola, third on the ellipse and the fourth on the hyperbola.

Important points of NCERT Class 11 Maths Chapter 11 Conic Sections-

  • Circle- It is the set of all points in the plane that are equidistant(or the same distance) from a fixed point in the plane. The fixed point is the centre of the circle and the distance from the centre to a point on the circle is the radius of the circle. The equation of a circle with centre (h, k) and the radius r is-

                                                         Conic Sections 

                                        \(x-h)^2+(y-k)^2=r^2

  • Parabola- It is the set of all points in the plane that are equidistant(or the same distance) from a fixed line and a fixed point (not on the line) in the plane. The fixed point F is the focus of the parabola and the fixed line is called the directrix of the parabola. If the coordinates of focus(F) is (a, 0) a > 0 and directrix x = – a, then the equation of the parabola is-

                                                      Conic sections-parabola

                                                             y^2=4ax

  • Ellipse- It is formed by a point, which moves in a plane in such a manner that the sum of its distances from two fixed points in a plane is constant. The two fixed points in the plane are called the foci of the ellipse. If the foci of the ellipse are on the x-axis, then the equation of an ellipse is-

                                                          Conic sections-Ellipse

                                                              \frac{x^2}{a^2}+\frac{y^2}{b^2}=1

  • Hyperbola- It is the locus of a point in a plane, which moves in such a manner so that the difference of whose distances from two fixed points in the plane is constant. The two fixed points in the hyperbola are called the foci of the hyperbola. If the foci of the hyperbola are on the x-axis, then the equation of a hyperbola is-

                                                Conic section-Hyperbola

                                                             \frac{x^2}{a^2}-\frac{y^2}{b^2}=1

Topics of NCERT Grade 11 Maths Chapter-11 Conic Sections

11.1 Introduction

11.2 Sections of a Cone

11.3 Circle

11.4 Parabola

11.5 Ellipse

11.6 Hyperbola

The complete Solutions of NCERT Class 11 Mathematics Chapter 11 is provided below:

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections - Exercise 11.1

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections - Exercise 11.2

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections - Exercise 11.3

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections - Miscellaneous

NCERT Solutions for Class 11 Mathematics

Chapter-1

Sets

Chapter-2

Relations and Functions

Chapter-3

Trigonometric Functions

Chapter-4

Principal 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-12

Introduction to Three Dimensional Geometry

Chapter-13

Limits and Derivatives

Chapter-14

Mathematical Reasoning

Chapter-15

Statistics

Chapter-16

Probability

NCERT Solutions for Class 11- Subject wise

NCERT Solutions for Class 11 Biology

NCERT Solutions for Class 11 Maths

NCERT Solutions for Class 11 Chemistry

NCERT Solutions for Class 11 Physics

 

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