Answer
$\frac{(x+1)^{2}}{12}+\frac{(y-4)^{2}}{16}=1$,
Work Step by Step
Distance between the center $(-1,4)$ and focus $(-1,6)$ is 2, which is the value of $c$.
$a^2=b^2-c^2=16-4=12$
$\frac{(x+1)^{2}}{12}+\frac{(y-4)^{2}}{16}=1$,
This is an equation of an ellipse.
