Parabola: Tangents and Midpoints of Chords

This GeoGebra applet demonstrates the geometric relationship between tangents and midpoints of chords on a parabola. By constructing the focus, tangent lines, chords, and their midpoints, it explores classical geometric properties of parabolas. The applet uses commands such as Parabola, Tangent, Intersect, Ray, Segment, Mirror, Midpoint, Polygon, and Translate to dynamically illustrate the connections between tangents at chord endpoints and the locus of midpoints of parallel chords. Students can interactively drag points along the parabola to observe how tangent lines, chord midpoints, and the focus relate to one another in real time. A key property highlighted is that the locus of midpoints of a family of parallel chords forms a ray parallel to the axis of symmetry of the parabola. Additionally, the applet shows that the tangent lines at the endpoints of any chord intersect on the line passing through the midpoint of the chord and parallel to the axis. This visualization reinforces fundamental results in conic geometry and supports deeper understanding of parabolic optics and reflection properties. The interactive nature allows learners to test conjectures, make observations, and develop intuition about the elegant structure underlying parabolic curves. It is particularly suitable for courses in analytic geometry and conic sections, helping students bridge algebraic derivations with geometric insight.