Constructing a Parabola in GeoGebra via Focus–Directrix and Locus

This example shows how to draw a parabola in GeoGebra by constructing points that satisfy the defining distance condition between a focus and a directrix (equivalently, a focus–directrix relation). The resulting set of points forms the parabola. Key math ideas include the geometric definition of a parabola (equal distance to focus and directrix), geometric constructions that support tangent/median-type reasoning, and the distance/measurement perspective that can later connect to differential calculus for tangent behavior. Construction strategy: create foundational objects using Point, Segment, Line, and Circle to set up the focus/directrix and auxiliary geometry; use OrthogonalLine to build perpendicular references; use Intersect to locate crucial intersection points; and finally apply Locus to generate the parabola as the trajectory of points meeting the constraint. The involved GeoGebra objects (e.g., A, F, h, C, f, c, i, and others shown in the construct) represent the essential geometric points and parameters that feed into the locus construction. Suitable for middle school through early university, especially for coordinate geometry, graphing, and introductory discussions of tangency.