Tangents on an Ellipse and Their Orthocenter Properties

This example demonstrates constructing tangents to an ellipse and exploring geometric properties such as the orthocenter of a triangle formed by tangent intersections and points on the ellipse. Core mathematical concepts include ellipses, tangent lines, intersections, orthocenters, and parametric equations. Construction highlights: the CurveCartesian command defines the ellipse parametrically, Tangent generates tangents at a moving point, Intersect finds intersection points with axes or auxiliary lines, and SurdText displays exact radical values. Key objects include parameter θ, ellipse parameters a and b, moving point P, tangent lines f and g, intersection points Q and R, orthocenter-related objects, and text labels. Suitable for high school or college analytic geometry courses to visualize dynamic tangent relationships on an ellipse.