Find the equation of the hyperbola whose foci are and the transverse axis is of the length 10.

Given: Foci are , the transverse axis is of the length 10

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

The transverse axis is of the length 10, i.e., 2a = 10

Therefore, a = 5

The foci are given at

A and B are the foci.

That means, , 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]