Answer
$(y-1)^2=12(x+1)$
Work Step by Step
Given: Directrix $x=-4$, Focus:$F(2,1)$
Let us consider the standard form for the parabola $(y-k)^2=4p(x-h)$ ; $x=-a$
with Vertices:$(h,k)$
Then, we have
$|x+4|=\sqrt{(x-2)^2+(y-1)^2}$
$\implies (x+4)^2=(x-2)^2+(y-1)^2$
This implies that $(y-1)^2=x^2+16+8x-x^2-4+4x$
and $(y-1)^2=12x+12$
Hence, $(y-1)^2=12(x+1)$
