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Intersection of a Sphere and a Quadric Surface

Intersection of a Sphere and a Quadric Surface
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2018-08-03 22:18
CircleSolid GeometryTransformation
In collections intersection: surface-surface, curve-curve
This example demonstrates the intersection of a sphere and a quadric surface, showing different types of intersection lines. Key mathematical concepts include spheres, quadric surfaces, and intersection lines. It uses commands like Sphere, IntersectPath, Intersect, Point, Line, Locus, etc., in GeoGebra. Suitable for high school geometry and solid geometry studies.

GeoGebra Commands & Parameters

  1. Sphere((K_x, 0, -3 + K_h), (K_x, 0, K_h)) → K
  2. IntersectPath(a, QuK) → d
  3. Intersect(zAxis, yAxis) → Inf
  4. Point(d) → A
  5. Line(Inf, A) → f
  6. Intersect(f, K, 2) → B
  7. Locus(B, A) → Ortslinie1
  8. Intersect(e, d) → C_x, D_x
  9. Intersect(b, d) → E_y, F_y
  10. Coefficients(d) → Koeff_d
  11. Intersect(f, K) → C, D
  12. Locus(C, A) → Ortslinie2
  13. Coefficients(QuK) → ListQu
  14. IntersectPath(e, j) → l
  15. IntersectPath(e, k) → m
  16. Sphere(((-λ_M), 0, (-0.81 * λ_M)), (0, 0, 0)) → K_p
  17. OrthogonalPlane(Q_p, l) → n
  18. IntersectPath(n, QuK) → p
  19. Intersect(f, n) → H
  20. Point(p) → P_P
  21. Line(Inf, P_P) → q
  22. Intersect(q, K_p, 2) → I
  23. Locus(I, P_P) → Ortslinie3
  24. Intersect(f, K, 1) → E
  25. IntersectPath(e, zyl) → g
  26. OrthogonalLine(KPKT, e) → s
  27. Intersect(s, zyl) → G,
  28. Intersect(g, K) → J, N, ,
  29. Intersect(s, K) → L, M
  30. OrthogonalPlane(L, s) → o
  31. IntersectPath(o, K) → r
  32. OrthogonalLine(M, s, space) → f_1
  33. OrthogonalLine(M, s, space) → g_1
  34. OrthogonalLine(M, s, space) → h_1
  35. OrthogonalLine(M, s, space) → i_1
  36. OrthogonalLine(M, s, space) → j_1
  37. OrthogonalLine(M, s, space) → k_1
  38. OrthogonalPlane(M, s) → t
  39. IntersectPath(t, zyl) → c_1

AI Drawing Prompt Reference

Draw the intersection lines of a sphere and a quadric surface, showing different types of intersections. The sphere is centered on the y-axis and touches the x-axis below. First, find the intersection curve of the sphere and the quadric surface, then determine the points where this curve intersects the z-axis and draw the locus of these points. Next, find the intersection point of the z-axis and y-axis, and draw a line through this point and the intersection curve. Finally, find the intersection points of this line with the sphere and draw the locus of these points.
The prompt above was compiled from the original drawing commands and is for reference only.