# Parabola as an envelope

- Author:
- Zoltán Kovács

- Topic:
- Parabola

Given are fixed point F and fixed line d (as defined by points A and B). P is an arbitrary point on d. Let b be the perpendicular bisector of F and P. Now the set of lines b are tangent to the red curve, the envelope of the family of lines b.
GeoGebra can compute the red curve by using the command

`Envelope[b,P]`

. It is fast enough to animate the red curve (namely, a parabola with focus point F and directrix d) in real time if the user drags any of the points A, B or F.