Locus of Midpoint of Focal Chord on a Parabola

This applet demonstrates the locus traced by the midpoint of a focal chord on a parabola as one endpoint moves along the curve. The core mathematical concepts include the definition of a parabola, focal chords, and the geometric interpretation of loci. Using GeoGebra commands Point (defining points), Line (drawing chords), Intersect (finding intersections), Segment (constructing line segments), and Midpoint (calculating midpoints), the dynamic construction reveals that the locus is precisely the directrix of the parabola. This example is ideal for high school coordinate geometry courses, helping students understand locus problems, master parametric methods for finding trajectory equations, and explore the relationship between focal chords and the directrix.