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