Answer
Answer $D$: $y=1.25$
Work Step by Step
$\bf{Step\text{ }1}$
Bring the equation in standard form:
$$\begin{align*}
15y+3x^2&=0&&\text{Write the original equation.}\\
3x^2&=-15y&&\text{Subtract }15y\text{ from each side.}\\
x^2&=-5y&&\text{Divide each side by }3.
\end{align*}$$
$\bf{Step\text{ }2}$
We identify the directrix. The equation has the form $x^2=4py$, where $p=-1.25$. The $\bf{directrix}$ is $y=-p$ or $y=1.25$.
The correct answer is Answer $D$.
