Constructing the Cardioid via Intersection Locus

This example demonstrates how to generate the classic cardioid curve by combining geometric intersection with a locus (trajectory) recording step. It highlights key mathematical ideas: parametric curve construction, trigonometric parameterization (cosine/sine-based angle-driven expressions), intersection-based constraints (finding points that satisfy multiple geometric relationships), and the locus concept—when a point moves under fixed rules, its path forms a curve. In GeoGebra, the construction uses Intersect to compute intersection points of the defining geometric objects, and then uses Locus to trace the resulting moving point (the curve). The involved objects/parameters include a, α, q, p, P, c, along with tx and ty to drive the parameter-dependent position of P. Suitable for high school to early university learners in coordinate geometry, trigonometry, and parametric equations, as well as for interactive exploration of how curves can be created from geometric constraints.