Question

Identify the equations of the asymptotes of the hyperbola (y - 7)2 - 16(x + 1)2 = 64.

Answer 1

`\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}\\\\ -------------------------------\\\\`


`\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)`