Geometric Construction of a Hyperbola with Mirror Symmetry and Asymptotes

This example demonstrates how to construct and visualize a hyperbola together with its key geometric features using interactive construction steps. By applying mirror symmetry and computing intersections, it builds the essential points and auxiliary lines that support the hyperbola’s structure. The core concepts include hyperbola geometry, asymptotes, mirror (reflection) transformations, line and segment construction, orthogonal lines, and intersection-based point determination, with distance measurements used to enforce geometric constraints. Construction is implemented with GeoGebra commands such as Line, Point, Mirror, Distance, Segment, Hyperbola, Asymptote, Slope, OrthogonalLine, Intersect, and Polygon, producing objects like the hyperbola and its asymptotes and a network of labeled points (e.g., O, F1, F2, C) and helper entities (e.g., reflected points and slope/auxiliary lines). Suitable for advanced secondary education and early university analytic geometry, especially for teaching hyperbola properties, symmetry-based constructions, and the geometric role of asymptotes.