In each of the following find the equations of the hyperbola satisfying the given conditions
foci (0, ±13), conjugate axis = 24
Given: foci (0, ±13) and the conjugate axis is 24
To find: equation of the hyperbola
Formula used:
The standard form of the equation of the hyperbola is,
Length of the conjugate axis is 2b
Coordinates of the foci for a standard hyperbola is given by (0, ±be)
According to question:
2b = 24 and be = 13
2b = 24
⇒ b = 12
⇒ b2 = 144
be = 12
We know,
a2 = b2(e2 – 1)
⇒ b2 = 25
Hence, the equation of the hyperbola is: