Find the center and radius of the circle $LaTeX: \displaystyle \left(x + 6\right)^{2} + \left(y - 8\right)^{2}=121$ .

Using the equation of a circle $LaTeX: \displaystyle (x-h)^2+(y-k)^2=r^2$ to identify $LaTeX: \displaystyle h,k,$ and $LaTeX: \displaystyle r$ gives: $LaTeX: \displaystyle h=-6$ , $LaTeX: \displaystyle k=8$ , and $LaTeX: \displaystyle r=11$ . The center is at $LaTeX: \displaystyle (-6,8)$ and the radius is $LaTeX: \displaystyle r = 11$ .