Check the picture below.
[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} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{[x-(-2)]^2}{6^2}+\cfrac{[y-(-6)]^2}{3^2}=1\implies \cfrac{(x+2)^2}{36}+\cfrac{(y+6)^2}{9}[/tex]
