[tex]\bf \textit{ellipse, vertical major axis}\\\\
\cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1
\qquad
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}, {{ k}}\pm a)\\
\textit{major axis}\ a+a=18\\
\qquad 2a=18\implies \boxed{a=9}\\
\textit{minor axis}\ b+b=10\\
\qquad 2b=10\implies \boxed{b=5}
\end{cases}
\\\\\\
\begin{cases}
h=0\\
k=0\\
a=9\\
b=5
\end{cases}\implies \cfrac{x^2}{5^2}+\cfrac{y^2}{9^2}=1[/tex]
check the picture below.
