NCERT Solutions for Class 11 Maths Chapter 10 Exercise 10.4 Conic Sections - PDF Download

NCERT solutions for class 11 maths chapter 10 exercise 10.4 Conic Section provides solutions for the curve hyperbola, a geometric shape that is both interesting and useful. Students will also deal with the standard equation of hyperbola, eccentricity of hyperbola and latus rectum of hyperbola. All these topics are explained in proper and detailed manner by the academic team of mathematics at eSaral. 

In-depth comprehension of topics included in ex 10.4 class 11 maths ch 10 will strengthen your knowledge to solve exercise questions. Class 11 maths chapter 10 exercise 10.4 NCERT solutions consists of 15 questions that helps students figure out how to solve equations for hyperbola and recognize different elements of it, like foci, vertices etc. Ex 10.4 class 11 maths ch 10 solutions can be downloaded in PDF version from eSaral. Download the free PDF of NCERT solutions to achieve high marks in exams. The link to download the PDF is provided below.

Topics Covered in Exercise 10.4 Class 11 Mathematics Questions 

Ex 10.4 class 11 maths chapter 10 is based on the topic of hyperbola, standard equation of hyperbola, latus rectum and eccentricity of hyperbola. You can get the detailed knowledge of these topics provided by the expert faculty of eSaral.

1. Hyperbola - A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant. 

• The term “difference” that is used in the definition means the distance to the farther point minus the distance to the closer point. 

• The two fixed points are called the foci of the hyperbola.

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

• The line through the foci is called the transverse axis and the line through the centre and perpendicular to the transverse axis is called the conjugate axis.

• The points at which the hyperbola intersects the transverse axis are called the vertices of the hyperbola.

• We denote the distance between the two foci by 2c, the distance between two vertices (the length of the transverse axis) by 2a and we define the quantity b as 

$\mathrm{b}=\sqrt{c^2-a^2}$

2. Eccentricity

Eccentricity of hyperbola is same like eccentricity of ellipse, the ratio $e=\frac{c}{a}$ is called the eccentricity of the hyperbola. Since c ≥ a, the eccentricity is never less than one. In terms of the eccentricity, the foci are at a distance of ae from the centre.

3. Standard equation of Hyperbola

The equation of a hyperbola is simplest if the centre of the hyperbola is at the origin and the foci are on the x-axis or y-axis.

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

4. Latus rectum

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

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

Tips for Solving Exercise 10.4 Class 11 Chapter 10 Conic Sections

NCERT solutions class 11 maths chapter 10 exercise 10.4 has some complex questions that need to be solved with proper understanding of concepts. Here, our math experts have combined some useful tips to solve these questions. You can check them below.

1. It is important for students to have a thorough understanding of the hyperbolic equation and how it can be applied to a number of sums.

2. NCERT solutions for class 11 maths chapter 10 ex 10.4 provided proper and precise understanding of concepts that students are familiar with the shape of a hyperbola and understand the special relationship between all points on the hyperbola.

3. To solve exercise questions, students must remember the formulas related to hyperbola, latus rectum and eccentricity.

Importance of Solving Ex 10.4 Class 11 Maths Chapter 10 Conic Sections

Here are some advantages that you can follow to solve ex 10.4 class 11 maths chapter 10 conic sections.

1. NCERT solutions for class 11 maths ch 10 give you a quick and easy way to solve every single question in exercise 10.4. It is a great way to make learning easier for you.

2. Ex 10.4 class 11 maths solutions have explained each topic in simple and precise language to help students understand the concepts easily.

3. NCERT solutions PDF for class 11 maths chapter 10 ex 10.4 have also included answers with questions that can help you to cross check your answers.

4. By practicing questions again and again and revising concepts will improve your problem solving abilities.

Frequently Asked Questions

Question 1. What is hyperbola in NCERT solutions class 11 maths chapter 10 ex 10.4?

Answer 1. A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is a constant.

Question 2. Write the standard equation of hyperbola?

Answer 2. The equation of a hyperbola 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 hyperbola?

Answer 3. The eccentricity of a hyperbola is the ratio of the distances from the centre of the hyperbola to one of the foci and to one of the vertices of the hyperbola.

Question 4. Write the latus rectum of hyperbola?

Answer 4. Length of the latus rectum of the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is $\frac{2 b^2}{a}$