Given: Vertices at (±6, 0) and foci at (±8, 0)

Need to find: The equation of the hyperbola.

Let, the equation of the parabola be:

Vertices of the parabola is at (±6, 0)

That means a = 6

The foci are given at (±8, 0)

A and B are the foci.

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

⇒ [As a = 6]

⇒

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒

⇒ [As a = 6]

So, the equation of the hyperbola is,

⇒ [Answer]