Chapter 11 Conic Sections Ex – 11.4

In each of the Exercises 1 to 6, find the coordinates of the foci and the vertices, eccentricity, and the length of the latus rectum of the hyperbolas.

Question 1.

\frac { { x }^{ 2 } }{ 16 } -\frac { { y }^{ 2 } }{ 9 } =1

Solution:

Given the equation of the hyperbola is

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 1

Question 2.

\frac { { y }^{ 2 } }{ 9 } -\frac { x^{ 2 } }{ 27 } =1

Solution:

Given the equation of the hyperbola is

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 2
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 3

Question 3.

9y2 – 4x2 = 36

Solution:

Given the equation of hyperbola is9y2 – 4x2 = 36

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 4

Question 4.

16x2 – 9y2 = 576

Solution:

Given equation of hyperbola is16x2 – 9y2 = 576

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 5

Question 5.

5y2 – 9x2 = 36

Solution:

Given equation of hyperbola is

5y2 – 9x2 = 36

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 6
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 7

Question 6.

49y2 – 16x2 = 784

Solution:

Given equation of hyperbola is49y2 – 16x2 = 784

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 8

In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given conditions.

Question 7.

Vertices (±2,0), foci (±3,0)

Solution:

Vertices are (±2, 0) which lie on x-axis. So the equation of hyperbola in standard form

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 9

Question 8.

Vertices (0, ±5), foci (0, ±8)

Solution:

Vertices are (0, ±5) which lie on x-axis. So the equation of hyperbola in standard form

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 10

Question 9.

Vertices (0, ±3), foci (0, ±5)

Solution:

Vertices are (0, ±3) which lie on x-axis. So the equation of hyperbola in standard form

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 11
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 12

Question 10.

Foci (±5, 0), the transverse axis is of length 8.

Solution:

Here foci are (±5, 0) which lie on x-axis. So the equation of the hyperbola in standard

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 13

Question 11.

Foci (0, ±13), the conjugate axis is of length 24.

Solution:

Here foci are (0, ±13) which lie on y-axis.

So the equation of hyperbola in standard

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 14

Question 12.

Foci (\pm 3\sqrt { 5 } ,0) , the latus rectum is of length 8.

Solution:

Here foci are (\pm 3\sqrt { 5 } , 0) which lie on x-axis.

So the equation of the hyperbola in standard

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 15
NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 16

Question 13.

Foci (±4, 0), the latus rectum is of length 12.

Solution:

Here foci are (±4, 0) which lie on x-axis.

So the equation of the hyperbola in standard

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 17

Question 14.

Vertices (+7, 0), e = \frac { 4 }{ 3 }

Solution:

Here vertices are (±7, 0) which lie on x-axis.

So, the equation of hyperbola in standard

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 18

Question 15.

Foci (0, \pm \sqrt { 10 } ), passing through (2, 3).

Solution:

Here foci are (0, \pm \sqrt { 10 } ) which lie on y-axis.

So the equation of hyperbola in standard form

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.4 19