SAT Question 267f82b5: Circles answer and explanation with Desmos solution

Choice B is correct. The equation of a circle in the xy-plane can be written as $(x-h{)}^2+(y-p{)}^2=r^2$, where the center of the circle is $(h,p)$ and the radius of the circle is $r$. It’s given that the circle in the xy-plane has the equation $(x-19{)}^2+(y-17{)}^2=64k^2$, where $k$ is a positive constant. It follows that $h=19$, $p=17$, and $r^2=64k^2$. Taking the positive square root of each side of $r^2=64k^2$ yields $r=8k$. Therefore, the center of the circle is at $(19,17)$ and the radius is $8k$.