Question

Find the standard form of the equation of the parabola with a focus at (0, -9) and a directrix y = 9.

Answer 1

The directrix is a horizontal line, and the focus lies below it. This means the parabola opens downward. The midpoint of (0, 9) (on the directrix) and (0, -9) will thus be the vertex of your paraboala. You can use all this info to write a parabola in the form
\[y=a(x-h)^2+k, \text{ where } (h,k) \text{ is the vertex.}\]

Answer 2

is y= -1/2x^2