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Chord of Contact from Directrix (H)

Chord of Contact from Directrix (H)
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2015-08-01 10:04
Coordinate GeometryGeometric ConstructionLocus
In collections Geometric Properties of Conics
This example demonstrates the property of the chord of contact drawn to the hyperbola from a point on the directrix. Key concepts include hyperbola, tangent, directrix, and point. Construction involves using GeoGebra commands like Point, Mirror, Hyperbola, Tangent, etc. Suitable for high school students learning coordinate geometry and geometric construction.

GeoGebra Commands & Parameters

  1. Point(h_1) → S
  2. Mirror(S, yAxis) → S'
  3. Point(xAxis) → A
  4. Hyperbola(S', S, A) → c
  5. Point(d) → D
  6. Tangent(D, c) → g, h
  7. Intersect(c, g) → P
  8. Intersect(c, h) → Q
  9. Segment(P, Q) → i
  10. Point(f) → D'
  11. Tangent(D', c) → j, k
  12. Intersect(c, k) → P'
  13. Intersect(c, j) → Q'
  14. Segment(P', Q') → l
  15. Line(P', Q') → r
  16. Mirror(A, yAxis) → A'
  17. Mirror(B, xAxis) → B'
  18. Line(B, xAxis) → a_1
  19. Line(B', xAxis) → b_1
  20. Line(A', yAxis) → c_1
  21. Line(A, yAxis) → d_1
  22. Intersect(a_1, c_1) → C
  23. Intersect(d_1, a_1) → E
  24. Intersect(b_1, c_1) → F
  25. Intersect(b_1, d_1) → G
  26. Polygon(C, E, G, F) → poly1, c_2, e_1, g_1, f_1