Parabola Locus: Construction with Tangents

This example demonstrates how to build and verify the locus behavior of a parabola using a coordinated set of lines, rays, perpendicular constructs, and intersection points, while also highlighting tangent relationships. The key math ideas include the definition of a parabola via locus (focal–directrix/constant-distance reasoning), locus construction, tangent geometry, and measuring angular relations at relevant points. Construction highlights: it uses Line, Point, and Segment to create the foundational geometric elements; Parabola to define the parabola itself; OrthogonalLine to enforce perpendicular constraints; Intersect to determine crucial intersection points; Ray and Angle to set and evaluate directed relations; and Tangent to construct the tangent line at the appropriate point on the parabola. The scene is organized around multiple named objects (including the parabola f), auxiliary points, and angle/annotation elements (e.g., α). Suitable for advanced high-school geometry and early university analytic/constructive geometry lessons, as well as student explorations focusing on parabola properties and dynamic geometric verification.