Hyperbola Definition: Foci, Distance Difference, and Dynamic Locus

① This example dynamically demonstrates the definition of a hyperbola: the locus of points where the absolute difference of distances to two fixed foci is constant. ② Core mathematical concepts include the geometric definition of a hyperbola, foci and transverse axis, the constant distance-difference condition, and the relationship to conic sections. ③ Construction highlights: using GeoGebra commands such as Hyperbola, Point, Circle, Segment, and Intersect to build the hyperbola, auxiliary circles, segments, and intersection points; dragging points or sliders to observe the changing locus, with text objects displaying the distance difference. ④ Suitable for high-school analytic geometry or introductory college conic sections, ideal for teacher demonstrations or student self-exploration of hyperbola properties.