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