Pedal Curve of a Parabola and Focus

①This example demonstrates the construction of the pedal curve of a parabola with respect to its focus, showing the locus of the foot of the perpendicular from the focus to each tangent of the parabola. ②Core mathematical concepts include pedal curves, parabola, focus, tangent and normal lines, and locus generation. ③Construction details: using GeoGebra commands Intersect, Point, Parabola, Ray, Tangent, OrthogonalLine, Angle, and Locus, with objects A, B, c, α, F, f, d, C, g, h, β, D, and locus loc1; the focus F and parabola f are defined, and the intersection D of tangent g and perpendicular h traces the locus. ④Suitable for high school or university courses in analytic geometry and differential geometry, useful for exploring curve families, envelopes, and the geometric meaning of pedal curves, as well as for dynamic geometry investigations.