Ellipse Reflective Property Dynamic Demonstration

This GeoGebra example dynamically demonstrates the reflective (optical) property of an ellipse: a ray emanating from one focus reflects off the ellipse and passes through the other focus. Core mathematical concepts include the focal definition of an ellipse, tangent lines, the law of reflection (angle of incidence equals angle of reflection), and coordinate geometry relationships. The construction employs GeoGebra commands such as Point, Vector, Tangent, Mirror, Segment, If, and Angle, along with objects including foci F₁ and F₂, a moving point P on the ellipse, tangent and normal lines, reflected rays, and angle markers α, β, γ, δ. It is suitable for high school analytic geometry, college calculus or precalculus courses, and physics optics modules focusing on geometric optics and conic sections.