In each of the, find the equations of the hyperbola satisfying the given conditions.

Vertices (0, 5), foci (0, 8)

Vertices (0, 5), foci (0, 8)

Here, the vertices are on the y-axis.

Thus,

The equation of the hyperbola is of the form

Since, the vertices are (0, 5), a = 5

Since, the foci are (0, 8), c= 8

We know that, a² + b² = c²

Thus, 5² + b² = 8²

⇒ b² = 64 – 25 = 39

Hence, the equation of the hyperbola is