In each of the following find the equations of the hyperbola satisfying the given conditions

vertices (± 2, 0), foci (± 3, 0)

Given: Vertices are (±2, 0) and foci are (±3, 0)

To find: equation of the hyperbola

Formula used:

The standard form of the equation of the hyperbola is,

Vertices of the hyperbola are given by (±a, 0)

Foci of the hyperbola are given by (±ae, 0)

Vertices are (±2, 0) and foci are (±3, 0)

Therefore,

a = 2 and ae = 3

⇒ 2 × e = 3

b² = a²(e² – 1)

⇒ b² = 5

The equation of hyperbola:

⇒ 5x² – 4y² = 20

⇒ 5x² – 4y² – 20 = 0

Hence, required equation of hyperbola is 5x² – 4y² – 20 = 0