[tex]\bf \begin{array}{llll}
\cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1\\\\ \cfrac{(x-{{ h}})^2}{{{ b}}^2}+\cfrac{(y-{{ k}})^2}{{{ a}}^2}=1
\end{array}\quad
\begin{cases}
\textit{major axis}=a+a\\
a=\textit{the larger denominator}\\
b=\textit{smaller denominator}
\end{cases}\\\\
-----------------------------\\\\
\cfrac{(x-7)^2}{4}+\cfrac{(y+3)^2}{16}=1\implies \cfrac{(x-7)^2}{2^2}+\cfrac{(y+3)^2}{4^2}=1\quad
\begin{cases}
a=4\\
b=2
\end{cases}[/tex]
