Witch of Agnesi: Locus Equation Construction

This GeoGebra example demonstrates the classic mathematical curve known as the Witch of Agnesi (or versiera), showing how its locus equation emerges from a dynamic geometric construction. The core mathematical concepts involve analytic geometry, locus equations, and parametric curves, with fundamental elements such as circles, lines, perpendiculars, and intersections. The construction uses GeoGebra commands: Circle, Line, Point, OrthogonalLine, Intersect, and LocusEquation. Specifically, a circle c is centered at point A, a horizontal line a passes through A, a moving point C lies on the circle, a perpendicular from C meets line a at D, and another perpendicular from D meets the vertical line b (through A) at E. The locus of point E as C moves along the circle is the Witch of Agnesi, and the LocusEquation command directly outputs its algebraic equation. This example is suitable for high school and university students studying analytic geometry, locus problems, or the history of mathematics, and can also serve as an introduction to classic curves in calculus courses.