Parabola Equation: Dynamic Focus-Directrix and Tangent Exploration

This GeoGebra example dynamically demonstrates the definition of a parabola: for any point P on the parabola, the distance to the focus F equals the distance to the directrix line d. It covers core concepts such as the standard equation of a parabola, focus and directrix, tangent line properties, and distance formula. The construction uses commands like Point, Segment, OrthogonalLine, Intersect, Distance, and Textfield to create the focus F, directrix d, moving point P, and its perpendicular foot D, while computing distances FP and PD. Input boxes allow adjusting parameters h, k, and p to update the parabola equation in real time. Text objects display distance values, and toggles showBlue/showPink control colored points for visual comparison. Ideal for high school analytic geometry, helping students grasp the parabola definition, parameter effects, and tangent derivation.