Given: Vertices are (±2, 0) and the eccentricity is 2

Need to find: The equation of the hyperbola.

Let, the equation of the hyperbola be:

Vertices are (±2, 0), that means, a = 2

And also given, the eccentricity, e = 2

A and B are the foci.

We know that,

Therefore,

⇒

⇒ [Squaring both sides]

⇒

⇒ [As a = 2]

So, the equation of the hyperbola is,

⇒ [Answer]