Answer
See below
Work Step by Step
A hyperbola with foci $( \pm 9,0)$ and vertices on the x-axis:
Since the vertices are at $(\pm 4,0) \rightarrow a=4$.
The foci are at $(\pm 9,0) \rightarrow ae=9$.
Rewrite the equation in standard form: $\frac{x^2}{4^2}-\frac{y^2}{9^2-4^2}=1\\\frac{x^2}{16}-\frac{y^2}{65}=1$
