Exploring the Geometric Definition of a Parabola

This interactive GeoGebra example demonstrates the geometric definition of a parabola: the set of all points equidistant from a fixed point (focus) and a fixed line (directrix). Students can explore how the parabola emerges as the locus of points satisfying PF = PD. Key mathematical concepts include focus, directrix, equidistance, and the relationship between the geometric definition and the standard quadratic equation. The construction uses GeoGebra commands such as Point to create the focus F and a point D on the directrix, OrthogonalLine to draw a perpendicular line, Intersect to find the moving point P, and Segment to display the distances PF and PD. Interactive buttons and checkboxes allow toggling the visibility of the focus, directrix, vertex, and distance segments, while sliders h, k, and c adjust the position and shape of the parabola. This resource is ideal for high school analytic geometry or introductory calculus courses, helping students visualize the definition and connect it to algebraic representations.