Answer
asymptotes: $y=\pm\frac{1}{3}(x+3)+4$
foci: $(-3\pm\sqrt {10},4)$
Work Step by Step
Step 1. Rewriting the equation as $\frac{(x+3)^2}{9}-\frac{(y-4)^2}{1}=1$, we have $a=3, b=1, c=\sqrt {a^2+b^2}=\sqrt {10}$ centered at $(-3,4)$ with a horizontal transverse axis.
Step 2. We can find the vertices as $(-6,4),(0,4)$ and asymptotes as $y-4=\pm\frac{b}{a}(x+3)$ or $y=\pm\frac{1}{3}(x+3)+4$
Step 3. We can graph the equation as shown in the figure with foci at $(-3\pm\sqrt {10},4)$
