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Polar Reciprocals: Parabola and Free Point

Polar Reciprocals: Parabola and Free Point
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2017-06-14 05:13
Coordinate GeometryTransformation
This example demonstrates the concept of polar reciprocals using a parabola and a free point. Key mathematical concepts include polar reciprocals, parabolas, and their properties. The construction uses GeoGebra commands such as Point, Circle, Parabola, Rotate, Ray, Intersect, Tangent, OrthogonalLine, Mirror, Locus, and Angle. Suitable for high school mathematics education, particularly in coordinate geometry and transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B_1
  2. Circle(C, 1) → d
  3. Parabola((0, 1), Line[(0, -1), (1, -1)]) → e
  4. Rotate(F, α, F) → A'
  5. Rotate(F + (0, -1), α, F) → B
  6. Ray(A', B) → f
  7. Intersect(e, f) → P,
  8. Tangent(P, e) → g,
  9. OrthogonalLine(C, g) → h
  10. Intersect(g, h) → E
  11. Mirror(E, d) → E'
  12. Locus(E', α) → loc1
  13. Locus(E, α) → loc2
  14. Angle(g, h) → β

AI Drawing Prompt Reference

Draw a parabola with its vertex at the origin and focus at (0,1), then rotate a point A around a point on the parabola, draw a ray from A, find its intersection with the parabola at point P, draw the tangent line at P, find the perpendicular line to this tangent, locate their intersection point E, mirror E across a given circle, and finally draw the loci of E and its mirror image E'.
The prompt above was compiled from the original drawing commands and is for reference only.