Given: Foci are (2, 0) and (-2, 0) and eccentricity is

To find: equation of the hyperbola

Formula used:

The standard form of the equation of the hyperbola is,

Center is the mid-point of two foci.

Distance between the foci is 2ae and b² = a²(e² – 1)

The distance between two points (m, n) and (a, b) is given by

Mid-point theorem:

Mid-point of two points (m, n) and (a, b) is given by

Center of hyperbola having Foci (2, 0) and (-2, 0) is given by

= (0, 0)

The distance between the foci is 2ae, and Foci are (2, 0) and (-2, 0)

b² = a²(e² – 1)

The equation of hyperbola:

⇒ 45x² – 36y² – 80 = 0

Hence, required equation of hyperbola is 45x² – 36y² – 80 = 0