Demonstrating Parabola, Focus, Directrix, and Vertex Relationship

This example demonstrates the definition of a parabola where any point's distance to the focus equals its distance to the directrix, dynamically showing the relationship between the vertex, focus, directrix, and the parabola itself. Core concepts include parabola definition, coordinate geometry, equidistance principle, right triangles, and reflection symmetry. Construction involves commands like Line, Parabola, Mirror, Intersect, Midpoint, and Prove to build and verify the geometric properties. Suitable for high school coordinate geometry teaching, math competitions, and geometric property exploration.