Parabola Geometric Construction: Focus-Directrix Definition

This GeoGebra example demonstrates the geometric construction of a parabola based on its focus-directrix definition: the locus of points equidistant from a fixed point (focus F) and a fixed line (directrix). Core mathematical concepts include conic sections, focus, directrix, perpendicular bisector, midpoint, tangent, and locus. The construction uses commands such as Line, Point, Segment, Midpoint, OrthogonalLine, Intersect, and Locus. Steps: create focus F and directrix g, choose a moving point D on the directrix, draw the perpendicular from D to the directrix, connect D to F, take the midpoint M_1 of DF, construct the perpendicular bisector of DF, and intersect it with the perpendicular through D to obtain point P. The Locus command traces P to generate the parabola. Additional elements like tangents, segments FP and EP, and auxiliary points are included. Suitable for high school analytic geometry or introductory college conic sections, ideal for exploring tangent properties and geometric constructions.