Parametric Curve and Right Triangle Locus Demo

Parametric Curve and Right Triangle Locus Demo
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2018-04-26 16:59
This example demonstrates the formation of parametric curves through dynamic parameter adjustment, focusing on the relationship between the locus and a right triangle within a cone. Core mathematical concepts include parametric equations, coordinate geometry, properties of right triangles, and conic geometry. GeoGebra commands and objects used in construction are Line, OrthogonalLine, Intersect, Segment, AngularBisector, and Angle. Suitable for high school and above students to understand parametric curve generation and geometric transformations.

GeoGebra Commands & Parameters

  1. Line(A, B) → AB
  2. Line(C, AB) → CD
  3. OrthogonalLine(P, AB) → c
  4. OrthogonalLine(P, CD) → d
  5. Intersect(AB, c) → G
  6. Intersect(CD, d) → H
  7. Segment(P, G) → e
  8. Segment(P, H) → f
  9. AngularBisector(AB, CD) → g, h
  10. OrthogonalLine(P, g) → L_2
  11. Intersect(g, L_2) → Q1
  12. Angle(P, H, C) → β
  13. Angle(P, G, B) → α