Question

Which equation represents a parabola that has a focus of (0, 0) and a directrix of y=−6 ?

Answer 1

Take any point (x,y) on the line 
distance between (x,y) and the focus = distance from the point to the directrix
s sqrt(x^2 + y^2)  = |x - (-6)|

x^2 + y^2 = x^2 + 12x + 36
y^2 = 12x + 36

that is the required equation