Find the equation of the hyperbola whose foci are and the eccentricity is .

Question

Philoid · Accepted Answer

Given: Foci are , and the eccentricity is

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

The eccentricity, e =

And also given, foci are

That means, ae =

⇒

⇒ [As e =]

⇒

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒ [As a = ]

So, the equation of the hyperbola is,

⇒ [Answer]