Parabola by geometric definition using Geogebra
A parabola can be defined as the locus of points equidistant from a point (the focus) and a line (the directrix). Drag point D along the line AB to watch point E trace out a parabola. Line AB is the directrix, and point C is the focus. E is on the perpendicular bisector of segment DC so it is equidistant from line AB and point C. (E is where a line perpendicular to AB at point D intersects the perpendicular bisector.)