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]