Question

Find the equation of the hyperbola with vertices at (0, ±5) and foci at (0, ±8).

Answer 1

Vertices are of the form (0, ±a), hence it is a vertical hyperbola.

So, the equation is of the form: y²/a² – x²/b² = 1 …..(1)

Given: vertices of hyperbola (0, ±5)

Here a = 5

Again,

Foci is of the form (0, ±c)

Given: foci of hyperbola at (0, ±8)

⇒ c = 8

Find b:

We know, c² = a² + b²

64 = 25 + b²

or b² = 39

Equation (1)⇒

y²/25 – x²/39 = 1

Which is required equation.