Question

Find the equation of the hyperbola satisfying the given conditions:

Foci (0, ±13), the conjugate axis is of length 24.

Answer 1

Foci (0, ±13), the conjugate axis is of length 24.

Here, the foci are on the y-axis.

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

Now foci are (0, ±13), c = 13.

Length of the conjugate axis is 24, 2b = 24 ⇒ b = 12

We know that a² + b² = c²

∴ a² + 12² = 13²

⇒ a² = 169 - 144 = 25

Thus, the equation of the hyperbola is `y^2/25 - x^2/144 = 1`.