Right Angle Subtended by Tangent and Directrix (Ellipse)

This applet dynamically illustrates a classic property of ellipses: the segment of the tangent between the point of contact and the directrix subtends a right angle at the corresponding focus. The core mathematical concepts involve conic sections, tangents, directrices, foci, and right-angle relationships, with implicit connections to isosceles triangles and parametric curves. The construction uses GeoGebra commands such as Point, Mirror, Ellipse, Intersect, Tangent, Segment, and Angle to build the ellipse, its foci and directrix, generate the tangent intersection, and display the angle measurement with text labels. Suitable for high school or early college students studying conic geometry, this applet serves as an interactive demonstration for teachers or a self-exploration tool for learners to visualize and verify the perpendicularity between the tangent and the directrix-related segment.