Parabola Construction: Focus, Directrix, and Locus

① This example demonstrates how to construct a parabola geometrically and use the locus tool to dynamically display the set of all points on the parabola. ② The core mathematical concept is the definition of a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix), involving conic sections, special points, and the relationship with trigonometric functions and real numbers. ③ Construction highlights: from the construction summary, the GeoGebra commands used include Line, Point, OrthogonalLine, LineBisector, Intersect, and Locus; objects include A, B, C, a, D, b, c, E, and the locus loc1. The process involves constructing the focus and directrix, then drawing perpendicular lines and perpendicular bisectors to find intersection points, finally generating the locus. ④ Suitable for high school or early college analytic geometry and conic sections teaching, also useful for dynamic demonstrations of the parabola definition, helping students intuitively understand the relationship between focus, directrix, and locus, and serving as a GeoGebra construction exercise.