Answer
asymptotes: $y=\pm\frac{5}{3}(x+2)+1$
foci: $(-2\pm\sqrt {34},1)$
Work Step by Step
Step 1. From the given equation $\frac{(x+2)^2}{9}-\frac{(y-1)^2}{25}=1$, we have $a=3, b=5, c=\sqrt {a^2+b^2}=\sqrt {34}$ centered at $(-2,1)$ with a horizontal transverse axis.
Step 2. We can find the vertices as $(-5,1),(1,1),(-2,0),(-2,2)$ and asymptotes as $y-1=\frac{b}{a}(x+2)$ or $y=\pm\frac{5}{3}(x+2)+1$
Step 3. We can graph the equation as shown in the figure with foci at $(-2\pm\sqrt {34},1)$
