Answer
$(y-2)^2=-12 (x -1)$
Work Step by Step
Since the directrix is a vertical line $4-1=3$ units to the right of vertex it means that the parabola is horizontal and facing left and $p=-3$.
The standard form of a vertical parabola vertical is given as: $(y-k)^2=4p(x-h) ~~~(1)$
Here, we have $(h,k)=(1,2)$, so $h=1; k = 2$.
Now, we will plug these values in equation (1) to obtain:
$(y-2)^2=(4)(-3) (x-1) \implies (y-2)^2=-12 (x -1)$
