Find the equation of the hyperbola with eccentricity and the distance between whose foci is 16.

Question

Philoid · Accepted Answer

Given: Eccentricity is , and the distance between foci is 16

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

Distance between the foci is 16, i.e., 2ae = 16

And also given, the eccentricity, e =

Therefore,

---- (1)

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒ [From (1)]

So, the equation of the hyperbola is,

⇒ ⇒ [Answer]