Circles SAT question

The correct answer is $16$. An equation of a circle in the xy-plane can be written as ${(x-t)}^2+{(y-u)}^2=r^2$, where the center of the circle is $(t,u)$ , the radius of the circle is $r$, and where $t$, $u$, and $r$ are constants. It’s given that the equation of circle A is ${(x+5)}^2+{(y-5)}^2=4$, which is equivalent to ${(x+5)}^2+{(y-5)}^2=2^2$. Therefore, the center of circle A is $(-5,5)$ and the radius of circle A is $2$. It’s given that circle B has the same center as circle A and that the radius of circle B is two times the radius of circle A. Therefore, the center of circle B is $(-5,5)$ and the radius of circle B is $2(2)$, or $4$. Substituting $-5$ for $t$, $5$ for $u$, and $4$ for $r$ into the equation ${(x-t)}^2+{(y-u)}^2=r^2$  yields ${(x+5)}^2+{(y-5)}^2=4^2$, which is equivalent to ${(x+5)}^2+{(y-5)}^2=16$. It follows that the equation of circle B in the xy-plane is ${(x+5)}^2+{(y-5)}^2=16$. Therefore, the value of $k$ is $16$.