Find the center and radius of the circle $LaTeX: \displaystyle \left(x - 10\right)^{2} + \left(y + 10\right)^{2}=49$ .

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: $LaTeX: \displaystyle h=10$ , $LaTeX: \displaystyle k=-10$ , and $LaTeX: \displaystyle r=7$ . The center is at $LaTeX: \displaystyle (10,-10)$ and the radius is $LaTeX: \displaystyle r = 7$ .