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