Dynamic Geometry Animation of Hyperbola and Circles: Tangents, Angles, and Trans

① This GeoGebra example demonstrates a dynamic animation involving a hyperbola, circles, tangents, angles, and various geometric transformations, showing interactions between conic sections and basic geometric elements. ② Core mathematical concepts include hyperbola (conic sections), circles, tangents, angles, midpoints, distances, dilation, rotation, as well as linear regression, inequalities, percentages, frequency distribution, and Pythagorean theorem, but the focus is on the geometric construction of hyperbola and circles. ③ Construction highlights: From the summary, commands such as Point, Ray, Midpoint, Intersect, Hyperbola, Distance, Circle, Segment, Tangent, CircleSector, Angle, Dilate, CircleArc, and Rotate are used, creating foci F_1 and F_2, hyperbola a, circles b and c, tangents d and e, plus auxiliary points, segments, arcs, and a button (button1) to control the animation. ④ Suitable for high school or early college courses in analytic geometry, conic sections, or dynamic geometry, and for teachers demonstrating hyperbola properties and geometric transformations visually.