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