recall that the major axis is "a + a" or 2a, whilst the minor axis is "b + b" or 2b.
so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.
[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}})
\end{cases}\\\\
-------------------------------\\\\
\textit{we know that }
\begin{cases}
a=\frac{30}{2}\\
b=\frac{14}{2}\\
h=-9\\
k=-7
\end{cases}\implies \cfrac{[x-(-9)]^2}{15^2}+\cfrac{[y-(-7)]^2}{7^2}=1
\\\\\\
\cfrac{(x+9)^2}{225}+\cfrac{(y+7)^2}{49}=1[/tex]
