Hyperbola from the Definition

① This GeoGebra example dynamically demonstrates the definition of a hyperbola: the locus of points where the absolute difference of distances to two fixed foci (F1, F2) is constant. ② Core mathematical concepts include conic sections, hyperbola definition, foci, vertices, transverse axis, and asymptotes. ③ Construction highlights: using commands such as Ray, Segment, Point, Line, Circle, Intersect, Rotate, Angle, Midpoint, and OrthogonalLine, the construction creates foci F1 and F2, vertices V1 and V2, a slider β, and a dynamic point P, along with auxiliary lines and circles to trace the locus satisfying the distance-difference condition. ④ Suitable for high school analytic geometry or college conic sections courses, this interactive tool helps students visualize the generation of a hyperbola and explore its properties, and can be used for classroom demonstrations or self-directed learning.