SAT Question 2855cb58: Circles answer and explanation with Desmos solution

Choice B is correct. The equation of a circle in the xy-plane can be written as $(x-h{)}^2+(y-k{)}^2=r^2$, where the center of the circle is $(h,k)$ and the radius of the circle is $r$. It's given that this circle has a center at $(16,17)$ and a radius of $7k$. Substituting $16$ for $h$, $17$ for $k$, and $7k$ for $r$ in $(x-h{)}^2+(y-k{)}^2=r^2$ yields $(x-16{)}^2+(y-17{)}^2=(7k{)}^2$, or $(x-16{)}^2+(y-17{)}^2=49k^2$. Therefore, the equation that represents this circle is $(x-16{)}^2+(y-17{)}^2=49k^2$.