Answer
$x^2=-\frac{4}{3}y$
Work Step by Step
We are given that the directrix is a horizontal line. This implies that the parabola is vertical.
The standard form of a vertical parabola is given as: $x^2=4py$ when vertex is centered at origin.
Here, the directrix is $y=-p \implies -p=\frac{1}{3} \implies p=-\frac{1}{3}$
Now, we have:
$$x^2=(4)\left(-\frac{1}{3}\right) y \\
\implies x^2=-\frac{4}{3}y$$
