Answer
$(y-3)^2=-\frac{1}{5}(x-2)$
Work Step by Step
1. Based on the given information, start from the standard equation $(y-k)^2=-4p(x-h)$
2. Given the center at $(2,3)$, we have $h=2,k=3$
3. Given point $(-18,1)$ on the curve, we have $(1-3)^2=-4p(-18-2)$, thus $p=\frac{1}{20}$
4. Thus the equation is $(y-3)^2=-\frac{1}{5}(x-2)$
