Question

Find the standard form of the equation of the parabola with a focus at (0, 8) and a directrix at y = -8.

Answer 1

so the focus is at (0, 8)

in a parabola the distance from the vertex to the focus is EXACTLY the same distance to the directrix

so the directrix is y=-8

focus is up, and directrix is down, the parabola opens up towards where the focus is, so this parabola opens upwards

since the focus and directrix are equidistant to the vertex, the vertex is half-way between both

from (0, 8) to y = -8, moving over the y-axis, the vertex is at the origin

Answer 2

the "focus form" for a parabola over the y-axis is \(\bf (x-h)^2=4p(y-k)\)

(h, k) = vertex point
p = distance from the vertex to the focus
p > 0, opens upwards
p < 0, opens downwards

Answer 3

thanks!