[tex]\bf \textit{hyperbola, vertical traverse axis }\\\\
\cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1
\qquad
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}, {{ k}}\pm a)\\
asymptotes\quad y={{ k}}\pm \cfrac{a}{b}(x-{{ h}})
\end{cases}\\\\
-------------------------------\\\\[/tex]
[tex]\bf (y-7)^2-16(x+1)^2=64\implies \cfrac{(y-7)^2}{64}-\cfrac{16(x+1)^2}{64}=1
\\\\\\
\cfrac{(y-7)^2}{64}-\cfrac{(x+1)^2}{4}=1\implies \cfrac{(y-7)^2}{8^2}-\cfrac{(x+1)^2}{2^2}=1
\\\\\\
\cfrac{(y-7)^2}{8^2}-\cfrac{[x-(-1)]^2}{2^2}=1\qquad
\begin{cases}
k=7\\
h=-1\\
a=8\\
b=2
\end{cases}
\\\\\\
y=7\pm\cfrac{8}{2}(x+1)[/tex]
