Inner Isoptics of a Hyperbola

① This example demonstrates the inner isoptics of a hyperbola—the locus of points from which the two tangents to the hyperbola subtend a constant angle. ② Core mathematical concepts include tangent properties of conics, angle measurement, parametric curves, and the use of derivatives and integrals to study curve families; it also involves analytic geometry and geometric transformations. ③ Construction: Based on the summary, GeoGebra commands such as Point, Tangent, Angle, Intersect, and Segment are used, with objects k (hyperbola), eq1 and eq2 (equations), u (parameter), A (moving point), f and g (tangent lines), α (fixed angle), B and C (tangency points), and h (locus curve). By moving parameter u or point A, the locus of A for a fixed α is traced, yielding the inner isoptics. ④ Suitable for high school to undergraduate courses in analytic geometry or calculus, this example helps visualize isoptic curves, tangent families, and locus generation, and can serve as material for mathematical experiments or inquiry-based learning.