Question

- 36y=x²
The directrix of the parabola is:
y=9
y=-9
x=9

Answer 1

`\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{`

`-36y=x^2\implies \stackrel{ 4p }{-36}(y-0)=(x-0)^2 \\\\\\ \stackrel{\textit{so we can say}}{4p=-36}\implies p=\cfrac{-36}{4}\implies p=-9`

now, the "p" distance is negative, meaning the parabola is clearly opening downwards like a camel's hump, that also means that the directrix is above it, and since the vertex is at the origin, Check the picture below.