Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 635: 3

The vertices are $(\pm4,0)$. The foci are $(\pm \sqrt{97},0)$.

The equation $$ \left(\frac{x}{4}\right)^{2}+\left(\frac{y}{9}\right)^{2}=1. $$ is hyperbola. We have $a=4$, $b=9$, $c=\sqrt{a^2+b^2}=\sqrt{97}$ and hence: The vertices are $(\pm4,0)$. The foci are $(\pm \sqrt{97},0)$.