SAT Question d03e29f1: Circles answer and explanation with Desmos solution

Choice C is correct. The equation of a circle in the xy-plane can be written as ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$, where the center of the circle is $(h,k)$ and the radius of the circle is $r$. The graph of the given equation, ${\left(x-6\right)}^2+{\left(y-3\right)}^2=81$, is a circle in the xy-plane. This equation can be written as ${\left(x-6\right)}^2+{\left(y-3\right)}^2=9^2$, where $h=6$, $k=3$, and $r=9$. Therefore, the radius of this circle is $9$.