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

vertices (0, ± 3), foci (0, ± 5)

Given: Vertices are (0, ±3) and foci are (0, ±5)

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 (0, ±b)

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

Vertices are (0, ±3) and foci are (0, ±5)

Therefore,

a² = b²(e² – 1)

⇒ a² = 16

The equation of hyperbola:

Hence, the required equation of the hyperbola is