Answer
asymptotes: $y= \pm\frac{3}{4}x$
foci: $(\pm15,0)$
Work Step by Step
Step 1. From the given equation $\frac{x^2}{144}-\frac{y^2}{81}=1$, we have $a=12, b=9, c=\sqrt {a^2+b^2}=15$ centered at $(0,0)$ with a horizontal transverse axis.
Step 2. We can find the vertices as $(\pm12,0)$ and asymptotes as $y=\frac{b}{a}x=\pm\frac{3}{4}x$
Step 3. We can graph the equation as shown in the figure with foci at $(\pm15,0)$
