Chapter 8.2, Problem 63.2PS

By expanding ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$, we obtain $x^2-2hx+h^2-2ky+k^2-r^2=0$. When we compare this result to the form $x^2+y^2+Dx+Ey+F=0$, we see that $D=-2h,E=-2k$, and $F=h^2+k^2-r^2$. Therefore, the center and the length of a radius of a circle can be found by using $h=\frac{D}{-2},k=\frac{E}{-2}$ and $r=\sqrt{h^2+k^2-F}$. Use these relationship to find the center and the length of the radius of each of the following circles.

$x^2+y^2+4x-14y+49=0$