Ellipse Standard Equation and Focus Properties

① This GeoGebra example dynamically demonstrates the standard equation of an ellipse and its geometric properties, visually showing that the sum of distances from any point on the ellipse to the two foci is constant. ② Core mathematical concepts include the definition of an ellipse (locus of points with constant sum of distances to two fixed points), parameters (semi-major axis a, semi-minor axis b, focal distance c), and elements such as center, foci, and vertices. ③ Construction details: Based on the summary, commands like Center, Segment, and Focus are used, creating objects h, a, k, b, c (parameters or lengths), points A, B, C, curves or segments d, e, auxiliary points D, E, and text labels text1, text2. These build the ellipse and its key features, possibly with sliders to adjust parameters. ④ Suitable for high school analytic geometry or introductory college geometry, helping students understand the ellipse definition, parameter relation (a² = b² + c²), and dynamic changes; useful for classroom demonstrations or self-exploration.