check the picture below.
so the ellipse looks more or less like that, notice the "a" component is 8 units, whilst the "c" component, namely the distance from the center to a focus is 7 units, thus
[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)\\
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=8\\
c=7
\end{cases}\implies \cfrac{(x- 0)^2}{ b^2}+\cfrac{(y- 0)^2}{ 8^2}=1
\\\\\\
c=\sqrt{a^2-b^2}\implies c^2=a^2-b^2\implies b^2=a^2-c^2
\\\\\\
b^2-64-49\implies b^2=15\qquad \qquad \cfrac{(x- 0)^2}{ 15}+\cfrac{(y- 0)^2}{ 8^2}=1
\\\\\\
\cfrac{x^2}{15}+\cfrac{y^2}{64}=1[/tex]
