Graphing Parametric Equations: Building Curves in Cartesian Coordinates

This example demonstrates how to plot parametric equations on a Cartesian plane to visualize the shape of parameterized curves (loci/trajectories). It focuses on the core idea that a curve is determined by coordinate functions (x(t), y(t)) and that varying parameters changes the resulting geometry. In GeoGebra, the construction uses the CurveCartesian command to create the curve from parameter-defined functions and associated parameters/constants. The construction summary indicates the use of function/object inputs f, g, parameters a, b, c, and a text label object (text1) to organize the mathematical definitions and provide clear annotations linking the plotted curve to its defining expressions. Suitable for secondary school through early undergraduate learners and for classroom demonstrations on graphing, loci, and parameter-driven geometry.