双曲面与圆的交线

GeoGebra 命令及参数

1. Surface((a * cos(v)) - ((a * u) * sin(v)), (a * sin(v)) + ((a * u) * cos(v)), (c * u), u, (-b), t, v, 0°, β) → g
2. CurveCartesian((a * sqrt(1 + u^(2))), ((a * sqrt(1 + u^(2))) * 0), (c * u), u, (-b), t) → i
3. CurveCartesian(a - ((a * u) * 0), (a * 0) + (a * u), (c * u), u, (-b), t) → j
4. OrthogonalLine(O, xOyPlane) → h
5. Sequence(Rotate[j, (i * 30°), zAxis], i, 0, β / (30°), 1) → l2
6. Sequence(Rotate[i, (k * 30°), zAxis], k, 0, α / (30°), 1) → l3
7. CurveCartesian(((a * sqrt(1 + t^(2))) * cos(v)), ((a * sqrt(1 + t^(2))) * sin(v)), (c * t), v, 0°, α) → k
8. CurveCartesian((a * cos(β)) - ((a * u) * sin(β)), (a * sin(β)) + ((a * u) * cos(β)), (c * u), u, (-b), t) → e
9. Surface(((a * sqrt(1 + u^(2))) * cos(v)), ((a * sqrt(1 + u^(2))) * sin(v)), (c * u), u, (-b), t, v, 0°, α) → d
10. CurveCartesian(((a * sqrt(1 + b^(2))) * cos(v)), ((a * sqrt(1 + b^(2))) * sin(v)), (c * (-b)), v, 0°, α) → l
11. Sequence(CurveCartesian[(a * cos((i * 30°))) - ((a * u) * sin((i * 30°))), ((-a) * sin((i * 30°))) - ((a * u) * cos((i * 30°))), (c * u), u, (-b), t], i, 0, β / (30°), 1) → l1
12. CurveCartesian(((a * sqrt(1 + u^(2))) * cos(α)), ((a * sqrt(1 + u^(2))) * sin(α)), (c * u), u, (-b), t) → f
13. Circle(O, a, xOyPlane) → p
14. CurveCartesian((((-a) * u) * 0), (a * u), (c * u), u, (-b), t) → a_1
15. CurveCartesian((((-a) * u) * sin(β)), ((a * u) * cos(β)), (c * u), u, (-b), t) → w
16. Rotate(a_1, 90°, h) → b_1
17. Rotate(b_1, α, h) → c_1
18. Surface((((-a) * u) * sin(v)), ((a * u) * cos(v)), (c * u), u, (-b), t, v, 0°, 360°) → g_1
19. CurveCartesian((((-a) * t) * sin(v)), ((a * t) * cos(v)), (c * t), v, 0°, 360°) → h_1
20. CurveCartesian((((-a) * (-b)) * sin(v)), ((a * (-b)) * cos(v)), (c * (-b)), v, 0°, 360°) → i_1
21. Point(xAxis) → A
22. OrthogonalPlane(A, xAxis) → p_1
23. Intersect(yAxis, p, 2) → B
24. Line(B, xAxis) → k_1
25. Intersect(k_1, p_1) → C
26. Line(C, A) → l_1
27. Point(l_1) → D
28. OrthogonalLine(D, p_1) → m_1
29. Circle(m_1, C) → q_1
30. Cylinder(q_1, -37.694964153002026) → n_1, r_1, o_1
31. Point(k) → E
32. Line(E, h) → s_1
33. Intersect(s_1, xOyPlane) → F
34. Vector(F, E) → u_1
35. Translate(B, u_1) → B'
36. Circle(h, B') → t_1
37. Tangent(E, t_1) → f_2, g_2
38. Circle(h, E) → c_2
39. Intersect(f_2, c_2, 1) → G
40. Vector(E, F) → v_1
41. Translate(G, v_1) → G'
42. Translate(G', v_1) → G''
43. Segment(E, G'') → h_2
44. Intersect(h_2, o_1) → H, I
45. Locus(H, E) → ponthalmaz1
46. Locus(I, E) → ponthalmaz2