Definition and Geometric Construction of a Parabola (Vertical)

This applet demonstrates the geometric definition of a parabola through an interactive, step-by-step construction. The user can place a focus point F and draw a directrix line p. The applet then uses a moving point on the directrix to construct the perpendicular bisector of the segment connecting the focus to that moving point. Each point on the parabola is defined as the set of points equidistant from the focus and the directrix. As the user drags the moving point along the directrix, the perpendicular bisector is drawn in real time, and the locus of the intersection points traces out a vertically oriented parabola. This visual animation clearly shows how the parabola emerges from the fundamental defining property: every point on the curve is at an equal distance from the focus and the directrix. The applet helps students understand the geometric essence of conic sections by making the abstract definition tangible. Students can explore how changing the position of the focus or rotating the directrix alters the shape and orientation of the resulting parabola. By observing the envelope formed by the family of perpendicular bisectors, learners gain insight into the reflective property of parabolas and their broader role within the family of conic curves. This hands-on exploration reinforces the connection between algebraic representations and geometric intuition, making it a valuable teaching tool for secondary and introductory college mathematics courses covering conic sections.