Answer
$(y-6)^2=28 (x+5)$
Work Step by Step
Since the directrix is a vertical line $-5-(-12)=7$ units to the left of the vertex, it means that the parabola is horizontal and facing right and $p=7$.
The standard form of a horizontal parabola is given as: $(y-k)^2=4p(x-h) ~~~(1)$
Here, we have $(h,k)=(-5,6)$, so $h=-5; k =6$
Now, we will plug these values in equation (1) to obtain:
$(y-6)^2=4 \times 7 [x-(-5)] \implies (y-6)^2=28 (x+5)$
