Answer
$\frac{x^2}{100}+\frac{y^2}{36}=1$
Work Step by Step
The equation of the ellipse here has the form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, where $a\gt b\gt0$, the vertices are at $(0,-a)$ and $(0,a)$.
Hence here by the text of the exercise, $a=\frac{20}{2}=10,b=6$, thus the equation is: $\frac{x^2}{10^2}+\frac{y^2}{6^2}=1\\\frac{x^2}{100}+\frac{y^2}{36}=1$
