Hyperbola 3b: Dynamic Construction via Circle and Perpendicular Bisector

This example demonstrates how to construct a hyperbola using a circle, points, and perpendicular bisectors, showcasing its standard geometric form. The core mathematical concept is the definition of a hyperbola as the locus of points where the absolute difference of distances to two fixed foci is constant, incorporating properties of circles, perpendicular bisectors, and locus generation. Construction details: using GeoGebra commands Circle, Point, and LineBisector, with objects A, c, B, C, and f, the dynamic interplay of a moving point on the circle and the perpendicular bisector of a segment ensures that distances satisfy the hyperbola condition, thereby tracing the curve. Suitable for high school analytic geometry or conic sections lessons, as well as introductory college geometry demonstrations, helping students intuitively grasp the generation mechanism and geometric essence of a hyperbola.