Question

Find the standard form of the equation of the parabola with a focus at (0, 6) and a directrix at y = -6.
PLEASE HELP ME

Answer 1

take any point (x,y) and then use the definition of parabola.

Answer 2

what @surjithayer

Answer 3

Let P (x,y) be any point on the parabola.
by definition PM=PF

Answer 4

keep in mind that the directrix in a parabola, is equally distant from the vertex as the focus, if the focus is at (0, 6) and the directrix is at y=-6 [ a flat horizontal line down below ], the vertex is half-way between them

also recall that a parabola "focus form" equation for a vertical opening parabola is \(\bf (x-h)^2=4p(y-k)\)

(h, k) = coordinates of the vertex
p = distance from the vertex to the focus/directrix