Question

Write an equation for the hyperbola with vertices (-7,0) and (7,0), conjugate axis of length of 10?

Answer 1

The hyperbola is more or less as in the picture below

notice the traverse axis is horizontal, meaning the positive fraction will be the one with the "x" variable in it, and notice the length of the "a" component

the conjugate axis is 10, notice the length of the  "b" component

thus    $\bf \textit{hyperbola with horizontal traverse axis }\\\\ \cfrac{(x-{{ h}})^2}{{{ a}}^2}-\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1 \qquad center\ ({{ h}},{{ k}})\qquad vertices\ ({{ h}}\pm a, {{ k}})$

so, hmmmm plug in those values