Polar Reciprocals: A Limaçon and A Hyperbola

Polar Reciprocals: A Limaçon and A Hyperbola
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2017-06-14 03:46
This example demonstrates the reciprocal relationship between a limaçon and a hyperbola through polar coordinate equations. Key math concepts include polar equations, reciprocal curves, geometric transformations, and analytical geometry. Construction highlights involve commands/objects like Point, Circle, Rotate, Tangent, OrthogonalLine, Angle, Intersect, Mirror, and Locus in GeoGebra. Suitable for high school and above students to explore the integration of polar coordinates and analytical geometry.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Point(xAxis) → B_1
  3. Circle(A, B_1) → c
  4. Point(xAxis) → C
  5. Circle(C, 1) → d
  6. Rotate(B_1, α) → B
  7. Tangent(B, c) → f, h
  8. OrthogonalLine(C, f) → g
  9. Angle(g, f) → β
  10. Intersect(f, g) → P'
  11. Mirror(P', d) → P
  12. Locus(P, α) → loc1
  13. Locus(P', α) → loc2