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NCERT Exemplar Class 11 Maths Chapter 11 Solutions: Conic Sections

NCERT Exemplar Solutions for Class 11 Maths Chapter 11 will help you study the equations of curved shapes such as circles, parabola, hyperbola, and ellipses. The NCERT Exemplar Class 11 Maths will prove to be essential for learning and building the confidence that is required to face the exams.

In NCERT Exemplar class 11 maths chapter 11, you will understand that the conic sections can be achieved by the intersection of a plane with a right circular cone. The main topics of chapter 11 are sections of a cone, parabola, hyperbola, ellipse, the focal distance of hyperbola, focal Distance of an ellipse, circle, equation of a circle, standard equations of parabola, the focal distance of a point of the parabola, directrix of the parabola, and parametric equation of conics.

There are 5 exercises with a total of 87 questions in Chapter 11 of conic sections. These problems will help you to understand the types of questions that will be asked in the exams. Also, the solutions provided by Instasolv will help you develop a mindset that is required in cracking tough exams.

Important Topics for NCERT Maths Exemplar Solutions Class 11 Chapter 11 – Conic Sections

Circles

The set of all points on a surface that is located at an equal distance from a fixed point in the plane is known as a circle.

  •  The equation of a circle with center (h, k) and the radius r is denoted by (p – h)2 + (q – k)2 = r2
  • The equation of a circle with center (0, 0) and the radius r is denoted by p2 + q2 = r2.
  • Features of the equation of a circle:
  1. Second degree in p and q
  2. Coefficient of p2 = coefficient of q2
  3. Coefficient of pq = 0

Parabola

The set of all points on a surface that is located at an equal distance from a fixed line and a fixed point on the surface is called Parabola. In geometric, Parabola is a locus of the point which keeps on moving so that its distance from a fixed point is similar to the distance from moving point to a fixed straight line.

The standard equation of the parabola with focus at (a, 0) a > 0 and directrix p = – a is q2 = 4ax.

Ellipse

The set of all points in a surface where the sum of whose distances from two fixed points in the surface is a constant. If the surface cuts completely across one nappe of the cone and Ɵ < α < 90 degrees, then the curve of intersection of cone and surface is an Ellipse.

An ellipse with foci on the x-axis can be represented in the form of p2/a2+ q2/b2 = 1

Hyperbola

The set of all points in a surface where the difference of whose distances from two fixed points in the surface is a constant is termed as a hyperbola.

A hyperbola with foci on the x-axis can be written in the form of the equation as follows: x2/a2 – y2/b2 = 1

Exercise-wise Discussion of NCERT Maths Exemplar Solutions Class 11 Chapter 11 – Conic Sections

Exercise 11.1 – Short Answer Type Questions

In this exercise of Chapter 11, there are a total of 22 questions that are based on the concepts of parabola, circles, and section of a cone.

Exercise 11.2 – Long Answer Type Questions

NCERT Exemplar Class 11 for Chapter 11 Exercise 11.2 contains a total of 10 questions. They are long answer type questions based on the ellipse, the focal distance of hyperbola, the focal Distance of an ellipse, circle, equation of a circle, standard equations of parabola, and focal distance of a point of the parabola. 

Exercise 11.3 – Objective Type Questions

This exercise consists of a total of 27 questions which are objective type questions based on the important topics related to the conic section. In these questions, you will be provided with 4 options and you have to choose the right answer. 

Exercises 4 and 5 consists of very short answer type questions including match the following, fill in the blanks and state true or false. Solving these questions will help you have prepared for the competitive exams as well.

Why Use NCERT Maths Exemplar Solutions Class 11 Chapter 11 – Conic Sections by Instasolv?

  • These NCERT exemplar solutions are prepared by the subject matter experts at Instasolv in order to guide you in your academics.
  • The exercise-wise solutions of the important topics of Chapter 11 – Conic Sections are available here on our web page, which you can easily follow at any time and from anywhere. 
  • These solutions are very useful for your conceptual knowledge and to build up problem-solving ability in yourself.

Referring to the NCERT exemplar class 11 maths solutions for chapter 11 will provide you with the basics and the advanced level of questions and answers that are mostly asked in various competitive exams.