Precalculus (6th Edition) Blitzer

Step 1. Graph the conic section as shown in the figure. Step 2. Rewrite the equation as $4(x^2+2x+1)-(y^2-2y+1)=4-1-7$ or $-(x+1)^2+\frac{(y-1)^2}{4}=1$. We can identify it is a hyperbola with $a=2,b=1,c=\sqrt {5}$ and center at $(-1,1)$. Step 3. We can find the foci at $(-1, 1\pm\sqrt {5})$ and the equations of the asymptotes as $y=\pm2(x+1)+1$