Question

PLEASE HELP WILL GIVE A MEDAL
Find the standard form of the equation of the parabola with a focus at (0, -10) and a directrix at y = 10

Answer 1

notice that focus point and that directrix
any ideas on where the vertext is at?

Answer 2

0,0? i really don't know

Answer 3

vertex is half-way between the directrix and focus point

Answer 4

but you'd be correct in this case, half-way between those 2 fellows, is 0,0

keep in mind that the parabola opens towards the focus point
in this case the focus point is down below, so the parabola opens dowwards

notice the distance from the vertex to either the focus or directrix?
that'd the distance "p"
the parabola goes down, thus "p" will be negative
and the equation will have a squared "x" variable
thus
\(\large {\begin{array}{llll}
(x-{\color{brown}{ h}})^2=4p(y-{\color{blue}{ k}})\\
\end{array}
\qquad
\begin{array}{llll}
vertex\ ({\color{brown}{ h}},{\color{blue}{ k}})\\
p=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}

\end{array} }\)

so, now you know what (h,k) are, and "p" as well, thus plug them in :)