Answer
$\dfrac{x^{2}}{12}+\dfrac{(y-4)^{2}}{16}=1$,
which represents an equation of ellipse.
Work Step by Step
Given: Vertices: $(0,0)$ and $(0,8)$
The midpoint of the vertices $(0,0)$ and $(0,8)$ is $(0,4)$ which is the center of the ellipse with $a^2=b^2-c^2=16-4=12$
Thus, $\dfrac{x^{2}}{12}+\dfrac{(y-4)^{2}}{16}=1$,
which represents an equation of ellipse.