Orthocentric Quadrilateral and Hyperbola Construction

This GeoGebra example demonstrates the geometric relationship between the orthocentric quadrilateral (four altitude feet of a triangle) and a hyperbola. Core mathematical concepts include triangle altitude properties, conic sections (hyperbola) definitions and equations, and the special geometric properties of the orthic quadrilateral. Construction steps: ① Create triangle vertices A, B, C using Point command; ② Construct the triangle with Polygon command; ③ Draw altitudes from each vertex to the opposite sides using OrthogonalLine command; ④ Find altitude feet with Intersect command to form the orthocentric quadrilateral; ⑤ Display the hyperbola and its relationship with altitude foot points. Suitable for high school coordinate geometry, conic sections, and plane geometry teaching, as well as college mathematics competition training.