Answer
$x^2=-\frac{5}{3}y$
Work Step by Step
If the parabola has its vertex at $(0,0)$ and its directrix at $y=-p$ then the equation is: $x^2=4py$.
Hence here $p=-\frac{5}{12}$, thus the equation is: $x^2=-\frac{5}{3}y$
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