Answer
asymptotes $y=\pm\frac{4}{5}x$
foci: $(\pm2\sqrt {41},0)$
Work Step by Step
Step 1. From the given equation $\frac{x^2}{100}-\frac{y^2}{64}=1$, we have $a=10, b=8, c=\sqrt {a^2+b^2}=2\sqrt {41}$ centered at $(0,0)$ with a horizontal transverse axis.
Step 2. We can find the vertices as $(\pm10,0)$ and asymptotes as $y=\frac{b}{a}x=\pm\frac{4}{5}x$
Step 3. We can graph the equation as shown in the figure with foci at $(\pm2\sqrt {41},0)$
