Question

write an equation for the parabola with the vertex at the origin and the directrix y=-1/48

Answer 1

\[x^{2}=-48y \]

Answer 2

y=12(x^2)

Answer 3

Thanks very helpful. :D

Answer 4

Whenever a problem involving a parabola mentions either focus or directrix, we need to use one of these two equations of a parabola:

4py=x^2

4px=y^2

...where p is the distance (a positive quantity) from the vertex to either the directrix or the focus. Both of these equations pertain to cases where the vertex is at the origin.

By re-reading the original problem statement, especially about the directrix, could you say whether the directrix is horiz. or vertical? Based upon that, could you say whether the parabola opens up, down, right or left?