Polar Defined Conic Sections

Polar Defined Conic Sections
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2012-06-05 06:23
This construction illustrates the polar form of conic sections, showing how conic curves are defined using polar coordinates. The core mathematical concepts include polar equations, eccentricity, focus and directrix, and classification of conic sections. The GeoGebra construction uses commands such as Segment, Midpoint, OrthogonalLine, Distance, CurveCartesian, and defines objects like F, C, a, M, b, B, c, ecc, d, P, e, f, D, g, distanceFB, etc., to build the polar representation. It is suitable for high school or early university mathematics courses, especially in analytic geometry and curve sketching.

GeoGebra Commands & Parameters

  1. Segment(F, C) → a
  2. Midpoint(a) → M
  3. OrthogonalLine(C, xAxis) → c
  4. Distance(F, B) → distanceFB
  5. Distance(B, C) → distanceBC
  6. Distance(F, C) → distanceFC
  7. CurveCartesian(ecc * distanceFC / (1 + ecc * cos(t)) * cos(t), ecc * distanceFC / (1 + ecc * cos(t)) * sin(t), t, 0, 6.283185307179586) → d
  8. Point(d) → P
  9. Segment(F, P) → e
  10. OrthogonalLine(P, c) → f
  11. Intersect(c, f) → D
  12. Segment(P, D) → g
  13. Distance(F, P) → distanceFP
  14. Distance(P, D) → distancePD