Drawing Parabola


Introduction

Parabola has following properties.

1.The distance from the point on the parabola to focus is equal to the distance to directrix.
(PF = PH)

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.


Applet

  • Drag the red point to make sure PF = PH.
  • If the distance of focus and directrix changes, what shape of parabola becomes?
    Press "+" or "-" button to consider.