Answer
$(y-1)^2=12(x+1)$
Work Step by Step
The general equation for the parabola is $(y-k)^2=4p(x-h)$; $x=-a$
Here, vertices: $(h,k)$
We are given that the Directrix is $x=-4$, Focus: $F(2,1)$
Thus, the equation of the parabola is:
$|x+4|=\sqrt{(x-2)^2+(y-1)^2}$
This implies that
$(x+4)^2=(x-2)^2+(y-1)^2$
or, $(y-1)^2=(x+4)^2-(x-2)^2$
or, $(y-1)^2=x^2+16+8x-x^2-4+4x$
or, $(y-1)^2=12x+12$
Thus, we have $(y-1)^2=12(x+1)$
