Find the equations of the hyperbola satisfying the given conditions : Foci $(0, \pm13)$, the conjugate axis is of length $24$.

Question

$\begin {array} {1 1} (A)\;\large\frac{x^2}{144}-\large\frac{y^2}{25}=1 & \quad (B)\;\large\frac{y^2}{25}-\large\frac{x^2}{144}=1 \\ (C)\;\large\frac{x^2}{144}+\large\frac{y^2}{25}=1 & \quad (D)\;\large\frac{x^2}{25}+\large\frac{y^2}{144}=1 \end {array}$