Answer
asymptotes: $y=\pm\frac{3}{2}x$
foci: $( \pm\sqrt {13},0)$
Work Step by Step
Step 1. Rewriting the equation as $\frac{x^2}{4}-\frac{y^2}{9}=1$, we have $a=2, b=3, c=\sqrt {a^2+b^2}=\sqrt {13}$ centered at $(0,0)$ with a horizontal transverse axis.
Step 2. We can find the vertices as $(\pm2,0)$ and asymptotes as $y=\frac{b}{a}x=\pm\frac{3}{2}x$
Step 3. We can graph the equation as shown in the figure with foci at $( \pm\sqrt {13},0)$
