MathPlotAI Logo MathPlotAI

Polar Conics with Eccentricity and Directrix

Polar Conics with Eccentricity and Directrix
Loading the math board and drawing, please wait…
2015-06-21 01:14
FunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Conics Doug Kuhlmann
This example demonstrates conic sections (ellipse, hyperbola, parabola) in polar coordinates, visually illustrating the geometric significance of eccentricity and directrix. Key math concepts include polar equations, eccentricity, directrix, and properties of quadratic curves. GeoGebra commands used are CurveCartesian for plotting, Vector for vectors, If for conditional logic, Max/Min for extrema, Textfield for text display, and SurdText for radical formatting. Suitable for high school coordinate geometry education, helping students grasp the definitions and properties of conic sections and enhancing mathematical modeling skills.

GeoGebra Commands & Parameters

  1. CurveCartesian((rc(t) * cos(t)), (rc(t) * sin(t)), t, 0, 6.283185307179586) → rcp
  2. Vector(rcp(θ)) → u
  3. If(togneg ≟ 0, "+", "-") → tgn
  4. If(togneg ≟ 1, "Change to +", "Change to -") → PlusMinus
  5. CurveCartesian((rs(t) * cos(t)), (rs(t) * sin(t)), t, 0, 6.28319) → rsp
  6. Vector(rsp(θ)) → w
  7. Max({x(Vc_1), x(Vc_2), x(Vs_1), x(Vs_2)}) → MaxX
  8. Min({x(Vc_1), x(Vc_2), x(Vs_1), x(Vs_2)}) → MinX
  9. Max({y(Vc_1), y(Vc_2), y(Vs_1), y(Vs_2)}) → MaxY
  10. Min({y(Vc_1), y(Vc_2), y(Vs_1), y(Vs_2)}) → MinY
  11. If(sn, x(Cs), x(Cc)) → xCen
  12. If(sn, y(Cs), y(Cc)) → yCen
  13. Max(abs(MaxX), abs(MinX)) → MX
  14. Max(abs(MaxY), abs(MinY)) → MY
  15. Textfield(ecc) → eEQ
  16. Textfield(dtrx) → dEQ
  17. Min(abs(y(Vs_1)), abs(y(Vs_2))) → FVs
  18. Min(abs(x(Vc_1)), abs(x(Vc_2))) → FVc
  19. If(SIGN < 0, Cs + (0, csi), Cs - (0, csi)) → Fs
  20. If(SIGN < 0, Cc + (csi, 0), Cc - (csi, 0)) → Fc
  21. SurdText(Cc) → CcValue
  22. SurdText(Cs) → CsValue