Answer
$(x+1)^{2}+(y-4)^{2}=4$
Work Step by Step
We know that the standard form of the equation of a circle with center $(h,k)$ and radius $r$ is $(x-h)^{2}+(y-k)^{2}=r^{2}$.
Therefore, we can plug in the given values for $h$, $k$, and $r$ and simplify.
$(x-(-1))^{2}+(y-4)^{2}=(2)^{2}$
$(x+1)^{2}+(y-4)^{2}=4$