NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.3 Conic Sections - PDF Download

NCERT solutions for class 11 maths chapter 10 exercise 10.3 Conic Sections talk about another curve which is an ‘ellipse’ that the students can explore in this exercise. This exercise also deals with the relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse. Students will be introduced to a new concept called the 'Eccentricity’ and In ex 10.3 class 11 maths chapter 10, we also have the standard equation of the ellipse and latus rectum of ellipse, which has been explained in detail.

Ex 10.3 class 11 maths solutions has a total of 20 questions which are solved in step by step by subject experts of eSaral. Class 11 maths chapter 10 exercise 10.3 NCERT solutions have been designed by an academic team of mathematics which provide accurate solutions to every topic and concept. NCERT solutions for class 11 maths chapter 10 ex 10.3 are also made available here in PDF format which can be downloaded easily from the official website of eSaral. Students can download these PDFs for free and practice all the questions and examples related to the exercise. The link to download the PDF is available below.

Topics Covered in Exercise 10.3 Class 11 Mathematics Questions 

Ex 10.3 class 11 maths chapter 10 Conic Sections is totally based on ellipse and standard equations of an ellipse, latus rectum of ellipse, eccentricity and relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse. All these topics are elaborated here by experts of eSaral.

1. Ellipse - An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant. The two fixed points are called the foci (plural of ‘focus’) of the ellipse.

• The mid point of the line segment joining the foci is called the centre of the ellipse. 

• The line segment through the foci of the ellipse is called the major axis and the line segment through the centre and perpendicular to the major axis is called the minor axis. 

• The end points of the major axis are called the vertices of the ellipse.

• We denote the length of the major axis by 2a, the length of the minor axis by 2b and the distance between the foci by 2c. Thus, the length of the semi major axis is defined as a and the semi-minor axis is defined as b.
  

2. Relationship between semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse

The lengths of semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse are related by the equation c² = a²-b²

3. Eccentricity - The eccentricity of an ellipse is the ratio of the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse. Eccentricity is denoted by ‘e’.

$e=\frac{c}{a}$

Then since the focus is at a distance of c from the centre, in terms of the eccentricity the focus is at a distance of ae from the centre.

4. Standard equations of an ellipse

The equation of an ellipse with foci on the x-axis is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

5. Latus rectum

Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse.

Length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\frac{2 b^2}{a}$

Tips for Solving Exercise 10.3 Class 11 Chapter 10 Conic Sections

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.3 has some queries related to finding the Equations of Ellipse under some conditions. To be well-versed with the concepts and to solve questions of ex 10.3, you must go through the tips provided by the expert faculty of eSaral.

1. It is recommended that the students read through the concepts thoroughly to comprehend the facts about the ellipse and also try to derive their equations using solved examples.

2. NCERT solutions class 11 maths chapter 10 ex 10.3 Conic Section also mentions some specific cases of the ellipse that the students need to be aware of. Students can also find the solutions in PDF if they have any doubts as it provides the information succinctly.

3. Before solving exercise questions, students should learn how to derive an equation of ellipse and remember the formula for clear understanding of questions.
   

Importance of Solving Ex 10.3 Class 11 Maths Chapter 10 Conic Sections

NCERT solutions class 11 maths ch 10 ex 10.3 provides you numerous benefits of solving questions. You can find here some of the benefits that can be used to understand the exercise.

1. NCERT solutions for class 11 maths chapter 10 ex 10.3 has questions which are solved in step by step manner to eliminate the confusion of students.

2. Ex 10.3 class 11 maths solutions have explained the concepts of ellipse, standard equations of an ellipse, latus rectum of ellipse precisely that will help you to solve the questions correctly.

3. Every question of ex 10.3 is solved in simple and easy language to help you complete this exercise with ease.

4. Practicing examples before ex 10.3 will help you to build a strong foundation of concepts in chapter 10 class 11 maths.

Frequently Asked Questions

Question 1. What is ellipse according to NCERT solutions class 11 maths chapter 10 ex 10.3?

Answer 1. An ellipse is the set of all points in a plane, the sum of whose distances from two fixed points in the plane is a constant. 

Question 2. Write the standard equation of an ellipse?

Answer 2. The standard equation of an ellipse with foci on the x-axis is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Question 3. What is the eccentricity of an ellipse

Answer 3. The eccentricity of an ellipse is the ratio between the distances from the centre of the ellipse to one of the foci and to one of the vertices of the ellipse.

Question 4. What is the latus rectum of an ellipse? write the length of the latus rectum of the ellipse.

Answer 4. Latus rectum of an ellipse is a line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse. 

Length of the latus rectum of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $\frac{2 b^2}{a}$