Hyperbola Resource: Foci, Asymptotes and Geometric Construction

① This example demonstrates the geometric construction of a hyperbola, using two foci F1 and F2 and the semi-transverse axis a to generate a moving point P on the hyperbola via circles and perpendicular bisectors, showing its locus. ② Core mathematical concepts include the definition of a hyperbola (the absolute difference of distances to two foci is constant 2a), the relationship between foci and transverse axis, asymptotes, and extensions to logarithms, rotation, and optimization. ③ Construction details: from the summary, the GeoGebra commands used are Circle, Intersect, Line, and LineBisector, with objects F1, F2, K, a, c, k, d, R, S, e, f, Q, P, g, D. The intersection of circles and perpendicular bisectors determines points on the hyperbola, and the locus tool generates the full curve. ④ Suitable for high school or early college analytic geometry courses, this resource helps students intuitively understand the definition, geometric properties, and dynamic changes of a hyperbola, and can be used for classroom demonstrations or self-study.