jmc

Completing the square, we can rewrite this equation as $(x+5{)}^2-25+(y+3{)}^2-9=k$, or $(x+5{)}^2+(y+3{)}^2=34+k$. Because this equation must represent a circle of radius 6, we need $34+k=6^2=36$, so $k=\boxed{2}$.