Proof of Hyperbolic Reflection

① This GeoGebra example demonstrates the construction and proof of hyperbolic reflection, visually showing how reflection preserves geometric and metric relationships on a hyperbola. ② Core mathematical concepts include hyperbola, reflection transformation, dilation, sequences and series, quadratic functions, hypothesis testing, and right triangle properties, integrating geometry with algebraic verification. ③ Construction highlights: based on the summary, it uses commands such as Segment, Point, Circle, Intersect, Midpoint, Line, Polygon, Angle, and Ray, with auxiliary objects including foci F_1, F_2, vertices V_1, V_2, and text labels (text1–text6) to annotate proof steps. ④ Suitable for high school to undergraduate geometry instruction, especially for analytic geometry, hyperbola properties, and transformation geometry, and for students to independently explore the mathematical essence of reflection.