# 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

Question 2.

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

Solution:

Given the equation of the hyperbola is

Question 3.

9y2 – 4x2 = 36

Solution:

Given the equation of hyperbola is9y2 – 4x2 = 36

Question 4.

16x2 – 9y2 = 576

Solution:

Given equation of hyperbola is16x2 – 9y2 = 576

Question 5.

5y2 – 9x2 = 36

Solution:

Given equation of hyperbola is

5y2 – 9x2 = 36

Question 6.

49y2 – 16x2 = 784

Solution:

Given equation of hyperbola is49y2 – 16x2 = 784

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

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

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

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

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

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

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

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

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