Question

Derive the equation of the parabola with a focus at(0,-4) and a directrix of y=4

Answer 1

SInce the focus is negative, this one opens downward.
Also, we can see that the focus and directrix are 4 units from the vertex, so p=4
Now for the equation we will use:
\(\Large\ y=-\frac{1}{4p}x^2\)
Plug in the value of p=4, which we have already found because the vertex is 4 units from the focus/directrix.