Hyperbola Equation Proof Interactive Demo

This GeoGebra example provides an interactive proof of the standard equation of a hyperbola. It demonstrates the geometric definition of a hyperbola as the set of points where the absolute difference of distances to two fixed foci is constant, and then derives the algebraic equation. The construction uses Segment and Intersect commands to create foci, vertices, and auxiliary points. Multiple buttons (button1-4) control step-by-step visualization, while text objects (text1-5) display key formulas and explanations. This resource is suitable for high school or early college students learning conic sections, and serves as a dynamic teaching tool for instructors or a self-study aid for learners.