## Calculus (3rd Edition)

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