Find the equation of the hyperbola whose foci are (±5, 0) and the conjugate axis is of the length 8. Also, find its eccentricity.
Given: Foci are (±5, 0), the conjugate axis is of the length 8
Need to find: The equation of the hyperbola and eccentricity.
Let, the equation of the hyperbola be:
The conjugate axis is of the length 8, i.e., 2b = 8
Therefore, b = 4
The foci are given at (±5, 0)
A and B are the foci.
That means, ae = 5, where e is the eccentricity.
We know that,
Therefore,
⇒
⇒
⇒ [Squaring both sides]
⇒
⇒
⇒
So, the equation of the hyperbola is,
⇒
Eccentricity, [Answer]