NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.1 Conic Sections - PDF Download

NCERT solutions for class 11 maths chapter 10 exercise 10.1 Conic Section, describes the sections of a cone with well illustrated diagrams and concepts such as upper nappe, lower nappe, generator and axis to provide a basis for understanding the curves and circle. This section further elaborates on the degenerate conic section. Additionally, students will learn an important equation relating to the circle.

Class 11 maths chapter 10 exercise 10.1 NCERT solutions comprises 15 questions, of which 11 are short questions and 4 are long answers questions. Ex 10.1 class 11 maths chapter 10 solutions are prepared by an academic team of mathematics with precise knowledge of the concepts associated with exercise 10.1 for students to score high marks in exams. Ex 10.1 class 11 maths solutions are also provided in PDF format. You can download the PDF for free from eSaral to make your learning simple to prepare for final examination. Download the PDF of NCERT solutions class 11 maths chapter 10 ex 10.1 from the link below.

Topics Covered in Exercise 10.1 Class 11 Mathematics Questions 

Ex 10.1 class 11 maths ch 10 is based on sections of a cone, degenerated conic sections and circle. You will get to know the detailed solutions of every topic from this exercise provided by our subject expert of eSaral.

1. Sections of a Cone

If we take the intersection of a plane with a cone, the section obtained is called a conic section. Thus, conic sections are the curves obtained by intersecting a right circular cone by a plane. 

We obtain different kinds of conic sections depending on the position of the intersecting plane with respect to the cone and by the angle made by it with the vertical axis of the cone. 

The intersection of the plane with the cone can take place either at the vertex of the cone or at any other part of the nappe either below or above the vertex. We made four different kinds of conic sections, namely:  Circle, ellipse, parabola and hyperbola.

• Circle, ellipse, parabola and hyperbola

When the plane intersects the nape of the cone (other than the vertex), we get the following situations:

(a) When β =90^o , the section is a circle.

(b) When α < β < 90^o , the section is an ellipse.

(c) When β = α; the section is a parabola.

In all three cases, the plane completely cuts across one nape of the cone.

(d) When 0 ≤ β < α; the plane cuts through both the nappes and the curves of intersection is a hyperbola.

• Degenerated conic sections

When the plane cuts at the vertex of the cone, there are the following different situations:

(a) When α < β ≤ 90^o , then the section is a point.

(b) When β = α, the plane contains a generator of the cone and the section is a straight line.

It is the degenerated case of a parabola.

(c) When 0 ≤ β < α, the section is a pair of intersecting straight lines, It is the degenerated case of a hyperbola. 

2. Circle - A circle is the set of all points in a plane that are equidistant from a fixed point in the plane.

The fixed point is called the centre of the circle and the distance from the centre to a point on the circle is called the radius of the circle.

With the Given (h, k) be the centre and r the radius of the circle, the equation of circle is

                                   (x – h)² + (y – k)² = r²

Tips for Solving Exercise 10.1 Class 11 Chapter 10 Conic Sections

Ex 10.1 class 11 maths solutions have some of the important tips to solve questions in exercise 10.1. You can check them all below.

1. NCERT solutions class 11 maths chapter 10 exercise 10.1 Conic Section is focused on the definition of the different kinds of curves and the way in which they are formed. Therefore, we suggest the students to revise their previous knowledge about cones in geometry as it will help them in understanding the current topic.

2. Ex 10.1 class 11 maths solutions has quite a number of new terms that the students need to be aware of.

3. Students need to practice drawing diagrams, which will help them get a better understanding of concepts and also they will remember the details more clearly.

4. The examples that are solved in the chapter are essential for the students to understand the facts, therefore, they should not miss them.
   

Importance of Solving Ex 10.1 Class 11 Maths Chapter 10 Conic Sections

There are a lot of advantages to solving questions of ex 10.1 class 11 maths chapter 10. Some of the benefits are described below.

1. NCERT solutions class 11 maths chapter 10 ex 10.1 covers important topics associated with sections of a cone, equation of circle, ellipse, parabola, hyperbola which provides deep understanding of concepts while solving the questions.

2. All the topics and concepts are elaborated in simple and easy to comprehend language so that you can solve the questions without any doubt.

3. NCERT solutions for ex 10.1 class 11 maths have also included examples and solved questions that will help you to prepare well for examinations.

4. Practicing with PDF solutions provided by eSaral, you can improve your problem solving skills.

Frequently Asked Questions

Question 1. What is a circle? write the equation of a circle.

Answer 1. A circle is the set of all points in a plane that are equidistant from a fixed point in the plane. The equation of the circle is (x – h)² + (y – k)² = r².

Question 2. What is the conic section in NCERT solutions class 11 maths chapter 10 ex 10.1?

Answer 2. If we take the intersection of a plane with a cone, the section obtained is called a conic section. There are four main types of conic sections in geometry that are Ellipse, Circle, Parabola and Hyperbola.