Standard Parabola with Focus, Directrix, and Tangent Dynamics

① This GeoGebra example dynamically illustrates the standard parabola y²=4ax, showing its focus, directrix, tangent and normal lines. ② Core mathematical concepts include conic sections (parabola), standard equation, focus-directrix definition, tangent slope via derivative, and geometric constructions of points and lines. ③ Construction uses commands: Point, OrthogonalLine, Intersect, Segment, If; objects include parameter a, focus F₁, equations eq1/eq2, dynamic text via FormulaText, and multiple text labels (text1–text9) to annotate properties. ④ Suitable for high school analytic geometry or introductory calculus, this interactive tool helps students visualize how the parameter a changes the parabola's shape and how tangent lines relate to the derivative, making it ideal for classroom demonstration or self-paced exploration.