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Intersection of Vertical and Horizontal Parabolas

Intersection of Vertical and Horizontal Parabolas
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2015-04-02 16:05
FunctionCoordinate GeometryInequalityGeometric Construction
This example demonstrates the intersection points between a vertical and a horizontal parabola. It involves core math concepts like parabolas, coordinate geometry, quadratic equations, and inequalities. The construction uses GeoGebra commands such as Parabola, Intersect, LineBisector, Vector, and Translate. Suitable for high school students learning coordinate geometry or educational demonstrations.

GeoGebra Commands & Parameters

  1. OrthogonalLine(B, yAxis) → a
  2. OrthogonalLine(D, xAxis) → b
  3. Parabola(C, b) → c
  4. Parabola(A, a) → d
  5. Intersect(c, d) → E, F, G, H
  6. Circle(E, F, G) → e
  7. LineBisector(F, G) → f
  8. LineBisector(H, G) → g
  9. Intersect(f, g) → I
  10. OrthogonalLine(A, a) → h
  11. OrthogonalLine(C, b) → i
  12. Intersect(b, i) → J
  13. Intersect(a, h) → K
  14. OrthogonalLine(C, a) → j
  15. OrthogonalLine(A, b) → k
  16. Intersect(a, j) → L
  17. Intersect(b, k) → M
  18. Intersect(a, b) → N
  19. Vector(K, A) → u
  20. Vector(M, A) → v
  21. Vector(L, C) → w
  22. Vector(J, C) → l
  23. OrthogonalLine(I, b) → m
  24. OrthogonalLine(I, a) → n
  25. Intersect(b, m) → O
  26. Intersect(a, n) → P
  27. Translate(P, u) → P'
  28. Vector(P, P') → p
  29. Translate(P', w) → P''
  30. Vector(P', P'') → q
  31. Translate(O, l) → O'
  32. Vector(O, O') → r
  33. Translate(O', v) → O''
  34. Vector(O', O'') → s

AI Drawing Prompt Reference

Draw the intersection points of a vertical parabola and a horizontal parabola. First, draw a vertical parabola with vertex C and y-axis as the axis of symmetry; then draw a horizontal parabola with vertex A and x-axis as the axis of symmetry. Find the intersection points E, F, G, H of these two parabolas, and draw circles with these points as centers. Find the tangents of these circles and their intersection point I. Then, draw parabolas with vertices A and C and axes of symmetry y-axis and x-axis, and find their intersections with the previous parabolas, J, K, L, M, N. Through vector translation and rotation, find points P, P', P'', O, O', O'', and draw vectors between them.
The prompt above was compiled from the original drawing commands and is for reference only.