Matching Parabola to Locus of Midpoint of Focal Chord

This example demonstrates the locus of the midpoint of a focal chord in a parabola. By adjusting the parabola's parameters, users can observe how the midpoint M traces a curve and verify its relationship with the original parabola. Core mathematical concepts include the definition of a parabola, focus, directrix, focal chord, and the derivation of the midpoint locus. Construction details: using GeoGebra commands such as Point, Line, Intersect, Midpoint, and Segment, the parabola c, focus A, and points B, C, D on the focal chord are constructed, with M as the midpoint. Sliders a, b, h, k control the parabola's equation, and text objects display dynamic values. Suitable for high school or college analytic geometry courses, this interactive tool helps students visualize the algebraic form of the midpoint locus and supports inquiry-based learning.