Answer
$\frac{(x+1)^{2}}{9} + \frac{(y-1)^{2}}{25} = 1$
Work Step by Step
General Equation of an ellipse is: $\frac{(x-h)^{2}}{b^{2}} + \frac{(y-k)^{2}}{a^{2}} = 1$
Vertices are (-1, -4) and (-1, 6), so the center is at the midpoint of the two points which is at (-1, 1). So h = -1, k = 1
From the center to the vertice, the distance is 5, thus a=5 (this value squared will be under y since the vertices are on a VERTICAL line)
Foci are (-1, -3) and (-1, 5), so c (the distance from focus to center) is equal to 4
$c^{2} = a^{2} - b^{2}$
$4^{2} = 5^{2} - b^{2}$
$b^{2} = 9$
Thus the answer is $\frac{(x+1)^{2}}{9} + \frac{(y-1)^{2}}{25} = 1$
