In each of the, find the equations of the hyperbola satisfying the given conditions.

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

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

Here, the foci are on y-axis.

Thus,

The equation of the hyperbola is of the form

Since, the foci are (0, 13), c= 13

Since, the length of the conjugate axis is 24,

2b = 24 ⇒ b = 12

We know that, a² + b² = c²

a² + 12² = 13²

⇒ a² = 169 – 144 = 25

Hence, the equation of the hyperbola is