Answer
$\dfrac{(x-4)^{2}}{25}+\dfrac{(y+1)^{2}}{9}=1$, which represents an equation of ellipse.
Work Step by Step
From the given points:
$c=\frac{8-0}{2}=4$
Thus, $b^2=a^2-c^2=25-16=9$
or, $\dfrac{(x-4)^{2}}{25}+\dfrac{(y+1)^{2}}{9}=1$,
which represents an equation of ellipse.