Focus and Directrix of a Parabola by Scott Geyer

This GeoGebra example dynamically illustrates the focus and directrix of a parabola, demonstrating that every point on the parabola is equidistant from the focus and the directrix. The core mathematical concepts include the definition of a parabola as a conic section, the geometric properties of focus and directrix, and distance measurement. Construction details: using the Intersect command to create intersection points between the parabola and auxiliary lines, and the Segment command to connect the focus, directrix, and related points, forming a draggable dynamic figure that allows observation of the constant distance relationship. Suitable for middle school (upper grades) or high school analytic geometry teaching, as well as introductory college geometry courses, helping students grasp the geometric essence of a parabola.