Geometric Construction of Tangent to a Parabola and Its Properties

① This example demonstrates how to construct a parabola and the tangent at an arbitrary point in GeoGebra, and to verify the geometric relationship between the tangent, focus, and directrix. ② Core mathematical concepts include the definition of a parabola, focus and directrix, tangent properties, perpendicular lines, midpoints, and geometric proof. ③ Construction highlights: Parabola to create the curve, Point to mark points, Tangent to draw the tangent line, OrthogonalLine for perpendiculars, Intersect to find intersections, Midpoint for midpoints, and Prove for automated geometric verification. ④ Suitable for high‑school analytic geometry lessons, university geometry demonstrations, and self‑directed exploration.