Answer
asymptotes: $y=\pm\frac{6}{7}(x+1)+2$
foci: $(-1,2\pm\sqrt {85})$
Work Step by Step
Step 1. From the given equation $\frac{(y-2)^2}{36}-\frac{(x+1)^2}{49}=1$, we have $a=6, b=7, c=\sqrt {a^2+b^2}=\sqrt {85}$ centered at $(-1,2)$ with a vertical transverse axis.
Step 2. We can find the vertices as $(-1,4),(-1,8)$ and asymptotes as $y-2=\pm\frac{a}{b}(x+1)$ or $y=\pm\frac{6}{7}(x+1)+2$
Step 3. We can graph the equation as shown in the figure with foci at $(-1,2\pm\sqrt {85})$
