Chapter 1 - Section 1.9 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 280: 35

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

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