Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 15

$$ \left(\frac{x}{3}\right)^{2}-\left(\frac{y}{4}\right)^{2}=1. $$

Since the vertices are $(\pm 3,0)$ and the foci are $(\pm 5,0)$, then we have $a=3, c=5 $, and hence $b=\sqrt{c^2-a^2}=\sqrt{25-9}=4$. Hence the equation of the hyperbola is given by $$ \left(\frac{x}{3}\right)^{2}-\left(\frac{y}{4}\right)^{2}=1. $$