Parabola has following properties.
1.The distance from the point on the parabola to focus is equal to the distance to directrix.
2.We define the coordinates of F,P and H as (a, b), (x, y) and (x, -b) respectively.
Since PF = PH
(x - a)2+(y - b)2 = (y + b)2
The equation of parabola is
y = (x - a)2/4b.