Constructing a Parabola Given Focus and Directrix

This GeoGebra example demonstrates how to construct a parabola from a given focus point and a directrix line, illustrating the fundamental definition of a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). The construction uses the Point command to place the focus F and a point D on the directrix, the Parabola command to generate the curve directly, and the Intersect command to find the vertex V and other intersection points with the axis. Key objects include the axis (asse), directrix (direttrice), and auxiliary segments and text labels. The example is ideal for high school analytic geometry lessons, helping students visualize the relationship between focus, directrix, vertex, and the parabola's shape. It can also serve as a quick demonstration in introductory college geometry courses.