We have the next information
Foci: (0,0), (0,8),
Mayor axis =10
Minor axis =6
We will use the next form of the equation of the parabola
[tex]\frac{(x-h)}{b^2}+\frac{(y-k)^2}{a^2}[/tex]
Then we need to know a and b
a=10/2=5
b=6/2=3
and the center is (0,4) in the middle of the points (0,0) and (0,8)
h=0
k=4
The equation of the ellipse is
[tex]\begin{gathered} \frac{\left(x\right)^{2}}{3^{2}}+\frac{\left(y-4\right)^{2}}{5^{2}}=1 \\ \frac{x^2}{9^{}}+\frac{(y-4)^2}{25}=1 \end{gathered}[/tex]
