Chapter 13 - Conic Sections - 13.1 Conic Sections: Parabolas and Circles - 13.1 Exercise Set - Page 854: 40

$(x+7)^2+(y+2)^2=50$

Using $(x-h)^2+(y-k)^2=r^2$ or the Center-Radius form of the equation of circles, the equation of the circle with center $( -7,-2 )$ and radius, $r= 5\sqrt{2} ,$ is \begin{array}{l}\require{cancel} (x-(-7))^2+(y-(-2))^2=\left( 5\sqrt{2} \right)^2 \\\\ (x+7)^2+(y+2)^2=25\cdot2 \\\\ (x+7)^2+(y+2)^2=50 .\end{array}