Question

Find the equation of the hyperbola satisfying the given conditions:

Vertices (0, ±3), foci (0, ±5)

Answer 1

Vertices (0, ±3), foci (0, ±5)

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, ±3), a = 3.

Since the foci are (0, ±5), c = 5.

We know that a² + b² = c².

∴ 3² + b² = 5²

= b² = 25 - 9 = 16

Thus, the equation of the hyperbola is `y^2/9 - x^2/16 = 1`.