jmc

We rewrite the equation as $x^2+8x+y^2-2y=8$ and then complete the square, resulting in $(x+4{)}^2-16+(y-1{)}^2-1=8$, or $(x+4{)}^2+(y-1{)}^2=25$. This is the equation of a circle with center $(-4,1)$ and radius 5, so the area of this region is $\pi r^2=\pi (5{)}^2=\boxed{25\pi }$.