Answer
$\frac{(y-4)^{2}}{49} - \frac{(x+1)^{2}}{32} = 1$
Work Step by Step
General Equation of a Hyperbola is: $\frac{(y-k)^{2}}{a^{2}} - \frac{(x-h)^{2}}{b^{2}} = 1$
If vertices are on the vertical axis
Center is (-1, 4), thus h = -1, p = -4
The distance between center and vertice (-1, -3) is 7, thus a = 7 under the y term (since it's vertical)
Foci distance from center to (-1, -5) is 9, thus c = 9
$c^{2} = 7^{2} + b^{2}$
$9^{2} = 7^{2} + b^{2}$
$32 = b^{2}$
Thus the equation is $\frac{(y-4)^{2}}{49} - \frac{(x+1)^{2}}{32} = 1$
