SAT Question c447367f: 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 $(19,18)$ and a radius of $9k$. Substituting $19$ for $h$, $18$ for $k$, and $9k$ for $r$ in $(x-h{)}^2+(y-k{)}^2=r^2$ yields $(x-19{)}^2+(y-18{)}^2=(9k{)}^2$, or $(x-19{)}^2+(y-18{)}^2=81k^2$. Therefore, the equation that represents this circle is $(x-19{)}^2+(y-18{)}^2=81k^2$.