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