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Locus of Intersection of Perpendicular Tangents to Parabola

Locus of Intersection of Perpendicular Tangents to Parabola
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2019-01-30 16:47
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates that the locus of points of intersection of two perpendicular tangents to a parabola is a straight line (i.e., the directrix). Key math concepts include parabola, tangent, locus, and coordinate geometry. It is constructed using GeoGebra commands like Tangent, Intersect, Angle, and Segment. Suitable for high school students and teachers exploring parabolic properties and geometric constructions.

GeoGebra Commands & Parameters

  1. Tangent(A, c) → g, h
  2. Intersect(c, g, 1) → B
  3. Intersect(c, h, 1) → C
  4. Angle(C, A, B) → α
  5. Segment(B, C) → j
  6. Intersect(j, xAxis) → D