Answer
$(y-1)^2=12(x+1)$
Work Step by Step
Here, we have Directrix $x=-4$ and Focus:$(2,1)$
Now, the equation of the parabola is equal to:
$|x+4|=\sqrt{(x-2)^2+(y-1)^2}$
After squaring, we get
$(x+4)^2=(x-2)^2+(y-1)^2 \implies (y-1)^2=(x+4)^2-(x-2)^2$
$(y-1)^2=x^2+16+8x-x^2-4+4x$
This gives: $(y-1)^2=12x+12$
Hence, our final result is: $(y-1)^2=12(x+1)$
