#### Answer

$(x+1)^2+(y-4)^2=4$

#### Work Step by Step

RECALL:
The standard equation of a circle whose center is at $(h, k)$ and has a radius of $r$ units is:
$(x-h)^2 + (y-k)^2 = r^2$
The given circle has its center at $(-1, 4)$ and a radius of 2 units.
Thus, the standard form of the circle's equation is:
$(x-(-1))^2+(y-4)^2=2^2
\\(x+1)^2+(y-4)^2=4$