Parabola: Reflective Property and Distance

①This example dynamically demonstrates the reflective property of a parabola: rays emanating from the focus reflect off the parabola parallel to the axis, and it also shows that the distance from any point on the parabola to the focus equals its distance to the directrix. ②Core mathematical concepts include the definition of a parabola (locus of points equidistant from a fixed point and a fixed line), focus, directrix, law of reflection, and geometric distance relationships. ③Construction highlights: using GeoGebra commands such as Sequence to generate a series of points, Point to mark the focus and points on the directrix, and Segment to connect the focus, points on the parabola, and reflected paths; auxiliary points (A, B, C, etc.) and segments (l1, l2, g, h, etc.) are constructed to visualize the reflection path and the constant distance property. ④Suitable for high school analytic geometry or introductory college geometry courses, this example helps students intuitively grasp the optical property of parabolas and the distance equality theorem, and can be used for mathematical experiments or inquiry-based learning.