check the picture below. So the ellipse looks more or less like so.
since the major axis is over the x-axis, is a horizontal ellipse, notice the "a" component length and the value for "c".
[tex]\bf \textit{ellipse, horizontal major axis}
\\\\
\cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1
\qquad
\begin{cases}
center\ ( h, k)\\
vertices\ ( h\pm a, k)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2- b ^2}
\end{cases}\\\\
-------------------------------[/tex]
[tex]\bf \begin{cases}
h=0\\
k=0\\
a=10\\
c=8
\end{cases}\implies 8=\sqrt{a^2-b^2}\implies 8^2=a^2-b^2\implies b^2=10^2-8^2
\\\\\\
b=\sqrt{100-64}\implies b=6
\\\\\\
\cfrac{(x-0)^2}{10^2}+\cfrac{(y-0)^2}{6^2}=1\implies \cfrac{x^2}{100}+\cfrac{y^2}{36}=1[/tex]
