Hyperbola Defined as a Set of Points

①This example dynamically demonstrates the definition of a hyperbola as the locus of points where the absolute difference of distances to two fixed foci is constant. ②Core mathematical concepts include the geometric definition of a hyperbola, foci, transverse and conjugate axes, and the generation of locus points via circle intersections and reflections. ③Construction highlights: using GeoGebra commands such as Sequence to generate parameterized points, Circle and Line to create auxiliary circles and lines, Mirror for symmetric reflection, and RemoveUndefined to clean invalid objects; key objects include B, λ, v_p, N, a, O, A, S1_1, l3, l1, d, Speed, C, f, g, l4, l5, l2, l2', l6, b, texte1, D, E, and image1. ④Suitable for high school analytic geometry or college conic sections courses, helping students visualize the hyperbola definition and the effect of dynamic parameters on the curve.