Focus and Directrix Parabola

①This GeoGebra example dynamically demonstrates the focus-directrix definition of a parabola, showing that every point on the parabola is equidistant from the focus and the directrix. ②Core mathematical concepts include the standard equation of a parabola, focus coordinates, directrix equation, vertex, axis of symmetry, and reflection properties, with extensions to similar triangles, area, and definite integrals. ③Construction highlights: using commands such as Segment, Line, Intersect, Point, and Root, the applet builds the vertex, focus, directrix, tangent lines, and auxiliary segments; sliders for parameters h, k, and p control the position and shape of the parabola, while multiple associated points (A, B, C, etc.) and text labels enable interactive exploration. ④Suitable for high-school analytic geometry or introductory college calculus, this resource helps learners grasp the geometric essence of conic sections, explore focus-directrix relationships, and connect to area and integral calculations.