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Rotating Polar Conics

Rotating Polar Conics
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2015-06-21 02:30
FunctionCoordinate GeometryTransformation
In collections Conics Doug Kuhlmann
This example demonstrates the dynamic changes of rotating polar conics. Key mathematical concepts include hyperbolas and parabolas in polar coordinates. Using GeoGebra commands such as CurveCartesian, Point, and Line, the generation process of the curves can be visually demonstrated. Suitable for high school mathematics education, particularly in coordinate geometry and curve transformations.

GeoGebra Commands & Parameters

  1. CurveCartesian((rd(θ) * cos(θ)), (rd(θ) * sin(θ)), θ, 0, 6.2831) → d_1
  2. Point(d_1) → B
  3. Point(d_1) → A
  4. Line(A, B) → g
  5. CurveCartesian((r(θ) * cos(θ)), (r(θ) * sin(θ)), θ, 0, 6.28319) → a
  6. OrthogonalLine(P, g) → h
  7. Intersect(g, h) → C
  8. Segment(P, C) → f
  9. Segment(P, F) → c