Parabola as an envelope
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.