Constructing a Parabola from Directrix and Focus (Geometric Method)

This example demonstrates how to construct points on a parabola using only geometric construction from a given directrix and focus, then trace the locus to reveal the curve. The core mathematical concept is the definition of a parabola: the set of points equidistant from a fixed point (focus) and a fixed line (directrix). The construction uses GeoGebra commands such as Line, Point, OrthogonalLine, Angle, Rotate, Intersect, and Segment to build isosceles triangles that enforce the equal-distance condition. Interactive buttons and sliders allow dynamic exploration, with a draggable point tracing the parabola. This is ideal for middle or high school geometry classes to visualize the parabola's definition and understand the relationship between geometric construction and locus generation.