Find the standard form of the equation of the parabola with a focus at (0, -10) and a directrix at y = 10.

Question

antonio_xx2 · Answer

@kirbykirby

kaylee_td · Answer

Please post this in the relevant section :)

antonio_xx2 · Answer

wait wut?

kaylee_td · Answer

This is called "openstudy feedback" not "Mathematics"

antonio_xx2 · Answer

@Kaylee_td  and i hope u become 1 and change the world;)

kaylee_td · Answer

Haha Thanks ;)

antonio_xx2 · Answer

and @Kaylee_td  we should talk some time:)

antonio_xx2 · Answer

u can stop now @kirbykirby  never mind

kirbykirby · Answer

So you have in general for the parabola:
$(x-h)^2 = 4p(y-k)$

The focus is represented by: $(h, k+p)$

And now to determine the sign of $p$, you notice that y=10 is the directrix, and the focus is at (0, -10), so the focus is below the directrix, meaning you should have a parabola having this shape $\cap$, so $p$ is negative

Focus: $(h, k+p))=(0, -10)$, so $h=0$ and $k+p =-10$
Now the vertex-focus distance is the same as the vertex-directrix distance, so it should be halfway. And so the you get that k =0, so p=-10

$(x-0)^2=4(-10)(y-0)$
$x^2=-40y$