Hyperbola Eccentricity Dynamic Demo

①This GeoGebra example dynamically demonstrates the geometric meaning of the eccentricity of a hyperbola, showing how changes in eccentricity affect the shape of the curve. ②The core mathematical concept is the eccentricity of a hyperbola, defined as the ratio of the focal distance to the semi-transverse axis (e = c/a), which determines the openness of the branches; it also involves the standard equation, foci, transverse axis, and conjugate axis of the hyperbola. ③Construction highlights: from the summary, objects such as r_x, r_y, c, r_f, e_c, and text1–text4 are used; likely sliders control the semi-transverse axis r_x and semi-conjugate axis r_y, the focal distance c is computed as √(r_x²+r_y²), then eccentricity e_c = c/r_x is calculated and displayed via text objects; the construction leverages GeoGebra's linked algebra and geometry views to update the graph and numerical values synchronously as parameters change. ④This is suitable for high-school analytic geometry lessons or introductory college math review, useful for classroom demonstrations of how eccentricity relates to hyperbola shape, and as an interactive exploration tool for students.