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Ellipse and Tangent Practice

Ellipse and Tangent Practice
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2022-05-14 11:14
FunctionCoordinate GeometryGeometric Construction
In collections Prime and Composite Numbers
This example demonstrates the construction of tangent lines to an ellipse and their relationship with the ellipse. Key math concepts include ellipse equations, tangent line equations, and derivative applications. GeoGebra commands and objects used in the construction are RandomElement, Polygon, IsPrime, IsInRegion, Sequence, Sum. It is suitable for high school coordinate geometry teaching and practice, helping students understand the geometric properties of curves and tangents.

GeoGebra Commands & Parameters

  1. RandomElement({4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25}) → c1, 24
  2. RandomElement({26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45}) → c2, 40
  3. RandomElement({46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64}) → c3, 60
  4. RandomElement({65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84}) → c4, 80
  5. RandomElement({85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100}) → c5, 85
  6. RandomElement({2, 3, 5, 7, 11}) → p1, 5
  7. RandomElement({13, 17, 19, 23, 29}) → p2, 13
  8. RandomElement({31, 37, 41, 43, 47}) → p3, 47
  9. RandomElement({53, 59, 61, 67, 71}) → p4, 61
  10. RandomElement({73, 79, 83, 89, 97}) → p5, 73
  11. RandomElement({c1, p1}) → a1, 5
  12. RandomElement({c2, p2}) → a2, 13
  13. RandomElement({c3, p3}) → a3, 47
  14. RandomElement({c4, p4}) → a4, 80
  15. RandomElement({c5, p5}) → a5, 85
  16. Polygon(A, B, C, D) → q1, a, b, c, d
  17. Polygon(E, F, G, H) → q2, e, f, g, h
  18. IsPrime(a1) → isa1prime
  19. IsInRegion(A_1, q1) → isa1inbox1
  20. IsInRegion(A_1, q2) → isa1inbox2
  21. IsInRegion(A_2, q1) → isa2inbox1
  22. IsInRegion(A_3, q1) → isa3inbox1
  23. IsInRegion(A_4, q1) → isa4inbox1
  24. IsInRegion(A_5, q1) → isa5inbox1
  25. IsInRegion(A_2, q2) → isa2inbox2
  26. IsInRegion(A_3, q2) → isa3inbox2
  27. IsInRegion(A_4, q2) → isa4inbox2
  28. IsInRegion(A_5, q2) → isa5inbox2
  29. IsPrime(a2) → isa2prime
  30. IsPrime(a3) → isa3prime
  31. IsPrime(a4) → isa4prime
  32. IsPrime(a5) → isa5prime
  33. Sequence(If[Element[anskey, i], 1, 0], i, 1, 5) → score, {0, 0, 0, 0, 0}
  34. Sum(score) → totalscore

AI Drawing Prompt Reference

Draw an ellipse and randomly select 5 points as its foci. Then, randomly choose 5 points as tangency points and draw the tangents at these points. Finally, randomly select two polygons and check if these tangency points are inside the polygons, and determine if the foci are prime numbers.
The prompt above was compiled from the original drawing commands and is for reference only.