Properties of Parabola: Focus, Directrix, and Tangent Reflection

This GeoGebra example dynamically illustrates the fundamental properties of a parabola, including its focus, directrix, tangent lines, and the reflection principle. It visually demonstrates that any point on the parabola is equidistant from the focus and the directrix, and uses tangent constructions to show how rays emanating from the focus reflect off the parabola parallel to its axis. The construction employs GeoGebra commands such as Point, Tangent, Line, Intersect, Segment, Ray, and Angle, with objects including the parabola, focus, directrix, tangents, and auxiliary points and angle markers. Suitable for high school analytic geometry or introductory college geometry, this resource helps students understand the definition of conic sections, tangent properties, and optical applications. It can serve as a classroom demonstration or an interactive exploration tool.