Exploring Parabola Properties: Focus, Directrix, Secants, and Geometric Construc

① This interactive GeoGebra example dynamically demonstrates key properties of a parabola, including its focus, directrix, secant lines, distance relationships, and associated angles and circumferences. ② Core mathematical concepts include the definition of a parabola (equal distances to focus and directrix), focal chord properties, secant-tangent relationships, applications of vectors and complex numbers in plane geometry, and measurement of distances, angles, and circumferences. ③ Construction highlights: using GeoGebra commands such as Point, Parabola, Segment, Distance, OrthogonalLine, Intersect, Angle, Circumference, PointIn, and Textfield, the construction includes focus F, directrix, point P1, secants, perpendicular lines, intersections, distance labels, circumferences, and text input boxes, with sliders and buttons for dynamic interaction. ④ Suitable for high school and early college students, this example serves as a teaching aid for analytic geometry and conic sections, and as a reference for teachers creating interactive lessons.