Chapter 11 – Conic Sections (Ex – 11.4)

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.
x²/16 − y²/9 = 1

Solution:
Given equation of hyperbola is

Question 2.
y²/9 − x²/27 = 1

Solution:
Given equation of hyperbola is

Question 3.
9y² – 4x² = 36
Solution:
Given equation of hyperbola is 9y² – 4x² = 36

Question 4.
16x² – 9y² = 576

Solution:
Given equation of hyperbola is 16x² – 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 (±3√5,0) , the latus rectum is of length 8.

Solution:
Here foci are (±3√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 = 4/3

Solution:
Here vertices are (±7, 0) which lie on x-axis.
So, the equation of hyperbola in standard

Question 15.
Foci (0, ±√10), passing through (2, 3).

Solution:
Here foci are (0, ±√10) which lie on y-axis.
So the equation of hyperbola in standard form