Relationship between Ellipse and Hyperbola

①This example demonstrates the intrinsic relationship between an ellipse and a hyperbola, showing how they share focal points and directrices while differing in eccentricity. ②Core mathematical concepts include conic sections, focus-directrix properties, eccentricity, and the transformation between ellipse and hyperbola under parameter changes. ③Construction details: Based on the summary, the construction uses GeoGebra commands such as Line, Point, Hyperbola, Intersect, LineBisector, and Ellipse, with objects A, B, a, C, c, D, b, E, d. Perpendicular bisectors and intersection points are used to define foci and directrices, from which both conics are generated. ④This is suitable for high school or college analytic geometry courses, serving as an interactive visual aid for teachers or as a student exploration tool to understand the unified nature of conic sections.