Find the equation of the hyperbola whose vertices are (0, ±3) and the eccentricity is . Also, find the coordinates of its foci.

Given: Vertices are (0, ±3) and the eccentricity is

Need to find: The equation of the hyperbola and coordinates of foci.

Let, the equation of the hyperbola be:

Vertices are (±3, 0), that means, a = 3

A and B are vertices.

And also given, the eccentricity, e =

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒ [As a = 3]

So, the equation of the hyperbola is,

⇒

Coordinates of the foci = (ae, 0) = (4, 0) [Answer]