SAT Question a5ff1a96: Circles answer and explanation with Desmos solution

Choice B is correct. An equation of a circle in the xy-plane can be written as $(x-h{)}^2+(y-k{)}^2=r^2$, where $(h,k)$ is the center and $r$ is the radius. It’s given that in the xy-plane, circle M is the graph of the equation $(x-4{)}^2+(y-5{)}^2=9$, which is equivalent to $(x-4{)}^2+(y-5{)}^2=3^2$. Therefore, the center of circle M is $(4,5)$ and the radius of circle M is $3$. It’s given that circle P has the same center as circle M but has a radius that is twice the radius of circle M. Therefore, the center of circle P is $(4,5)$ and the radius of circle P is $2(3)$, or $6$. Substituting $4$ for $h$, $5$ for $k$, and $6$ for $r$ in the equation $(x-h{)}^2+(y-k{)}^2=r^2$ yields $(x-4{)}^2+(y-5{)}^2=6^2$, which can be rewritten as $(x-4{)}^2+(y-5{)}^2=36$.