Quadratic Locus Equation: Demonstrating GeoGebra's LocusEquation Command with a

This example demonstrates the use of GeoGebra's LocusEquation command by constructing a parabola from its synthetic definition, showing how the algebraic equation of a locus can be automatically derived from geometric conditions. The core mathematical concept is the locus definition of a conic section (parabola) as the set of points equidistant from a fixed point (focus) and a fixed line (directrix), along with the relationship between geometric construction and its algebraic representation. The construction involves using Line and Point commands to create the base line and point, then LineBisector, OrthogonalLine, and Intersect to build the moving point satisfying the parabola's definition, followed by Locus to generate the curve, and finally LocusEquation to output its equation. This is suitable for high school or early college students learning analytic geometry, and serves as a powerful teaching tool for demonstrating the connection between dynamic geometry and symbolic algebra.