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Polar Reciprocals: Limaçon (no loop) and Ellipse

Polar Reciprocals: Limaçon (no loop) and Ellipse
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2017-06-14 04:07
Coordinate GeometryGeometric ConstructionLocus
This example demonstrates the polar reciprocals of a limaçon (no loop) and an ellipse. Key mathematical concepts include polar coordinates, limaçons, and ellipses. Using GeoGebra commands such as Point, Circle, Rotate, and Tangent, these shapes are constructed. Suitable for high school mathematics education or students learning coordinate 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