Question

Write the equation in standard form for the parabola with vertex (0,0) and directrix y=-6

Answer 1

This is a parabola which  has vertex at the origin and opens upwards.

general form  is x^2 = 4ay   where a is the focus

the focus is the same distance from the vertex as the directrix  So it is at the point (0, 6)

required equation is x^2 = 4*6 y

or y = (1/24) x^2