Answer
See graph and explanations.
Work Step by Step
Step 1. Graph the equation as shown in the figure.
Step 2. Rewrite the equation as $4(x^2+2x+1)-(y^2-6y+9)=4-11-9$ or $-\frac{(x+1)^2}{4}+\frac{(y-3)^2}{16}=1$; we have $a=4, b=2$ and thus $c=\sqrt {4^2+2^2}=2\sqrt {5}$
Step 3. As the center of the ellipse is at $(-1,3)$ and the major axis is vertical, the foci are $(-1, 3\pm2\sqrt {5})$ and the asymptotes are $y-3=\pm \frac{4}{2}(x+1)$ or $y=\pm 2(x+1)+3$ as shown in the figure.
