Ellipse and Hyperbola Review: Dynamic Construction of Foci, Vertices, and Asympt

① This GeoGebra applet provides a comprehensive review of the constructions for ellipses and hyperbolas, dynamically displaying the key elements such as foci, vertices, major/minor axes, and asymptotes. ② The core mathematical concepts covered include the definitions of ellipses and hyperbolas (constant sum/difference of distances from foci), focal length, major and minor axes, asymptote equations, and the geometric relationships between these components. ③ Construction highlights: based on the summary, the applet uses the Ellipse command to generate the conic, Asymptote for hyperbola asymptotes, SecondAxisLength and MajorLength to define axis dimensions, OrthogonalLine for perpendicular constructions, and Line, Intersect, Segment, Point, Vector, and If commands to build auxiliary points, lines, and conditional displays. ④ This resource is suitable for high school or early college analytic geometry courses, serving as a review tool for students to explore how changing parameters affects the shape and orientation of ellipses and hyperbolas, and for teachers to demonstrate key properties interactively.