Given: Vertices at (0, ±5) and foci at (0, ±8)

Need to find: The equation of the hyperbola.

Let, the equation of the parabola be:

Vertices of the parabola are at (0, ±5)

That means a = 5

The foci are given at (0, ±8)

A and B are the vertices. C and D are the foci.

That means, ae = 8, where e is the eccentricity.

⇒ [As a = 5]

⇒

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒

⇒ [As a = 5]

So, the equation of the hyperbola is,

⇒ [Answer]