If \( x^{2}=-16y \) is an equation of parabola then:$$\begin{aligned} \text{(A)} & \quad \text{directrix is } y=4 \\ \text{(B)} & \quad \text{directrix is } x=4 \\ \text{(C)} & \quad \text{co-ordinates of focus are } (0,-4) \\ \text{(D)} & \quad \text{co-ordinates of focus are } (-4,0) \\ \text{(E)} & \quad \text{length of latus rectum } = 16 \end{aligned}$$ choose correct option
Explanation:
The given parabola is
\[
x^{2} = -16y
\]
Standard form of a vertical parabola opening downwards is
\[
x^{2} = -4ay
\]
Comparing, we get
\[
4a = 16 \;\; \Rightarrow \;\; a = 4
\]
Key elements:
\[ \therefore \;\; \text{Correct options are (A), (C), and (E).} \]
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