Question

Find the equation of the hyperbola satisfying the given conditions:

Vertices (0, ±5), foci (0, ±8)

Answer 1

Vertices (0, ±5), foci (0, ±8)

Here, the vertices are on the y-axis.

Therefore, the equation of the hyperbola is of the form `y^2/a^2 - x^2/b^2 = 1`.

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

Since the foci are (0, ±8), c = 8.

We know that a² + b² = c².

∴ 5² + b² = 8²

b² = 64 - 25 = 39

Thus, the equation of the hyperbola is `y^2/25 - x^2/39 = 1`.