抛物线与圆的交点

抛物线与圆的交点
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2015-03-16 01:14
本范例演示了抛物线与圆的交点。核心数学概念包括解析几何中的曲线交点、根的求解和垂直线的构造。通过使用GeoGebra命令如Point、Circle、Root、OrthogonalLine等,可以直观地展示交点的动态变化。适合高中数学教学,特别是解析几何和函数图像的学习。

GeoGebra 命令及参数

  1. Point({h, k}) → O
  2. Circle(O, d) → c
  3. Root(g) → A, B, C, D, F, G
  4. OrthogonalLine(A, e) → i
  5. OrthogonalLine(B, e) → l
  6. OrthogonalLine(C, e) → m
  7. OrthogonalLine(D, e) → a_1
  8. Intersect(f, l, (2.9868060725339998, -2.982346512378994)) → H_1
  9. Intersect(f, l, (2.9868060725339998, -2.982346512378994)) → I_1
  10. Intersect(f, m, (8.314549691799938, -7.403901038585482)) → M
  11. Intersect(f, a_1, (25.359085660117678, 17.78529354637122)) → N
  12. Intersect(f, i, (0.41291792669726235, 10.399494905323442)) → E
  13. OrthogonalLine(G, e) → j
  14. OrthogonalLine(F, e) → b_1
  15. Intersect(f, b_1, (8.154731189963634, -3.3615622611948153)) → J
  16. Intersect(f, j, (9.768321159071533, -3.126750114223364)) → K
  17. Point(yAxis) → L_1
  18. Point({b, 0}) → P_1
  19. Point({0, o + a}) → Q
  20. Line(P_1, Q) → c_1
  21. Function(f, 0, 100) → g_1
  22. Point({0, (-a)}) → L
  23. Point({0, k}) → H
  24. OrthogonalLine(H, d_1) → e_1
  25. Point({h, k}) → I
  26. Segment(L, H) → h_1
  27. Segment(H, I) → i_1
  28. Segment(I, L) → j_1
  29. Midpoint(j_1) → R
  30. Circle(R, I) → k_1
  31. Circle(L, v) → p_1
  32. Intersect(k_1, p_1) → S, P, ,
  33. Circle(I, P) → q_1
  34. Intersect(r_1, s_1) → T, U, V, W, Z, A_1
  35. OrthogonalLine(T, s_1) → t_1
  36. OrthogonalLine(U, s_1) → a_2
  37. OrthogonalLine(V, s_1) → b_2
  38. OrthogonalLine(W, s_1) → c_2
  39. OrthogonalLine(Z, s_1) → d_2
  40. OrthogonalLine(A_1, s_1) → e_2
  41. Intersect(f, e_2, (9.768321159071533, -3.126750114223364)) → B_1
  42. Intersect(f, d_2, (8.154731189963634, -3.3615622611948153)) → C_1
  43. Intersect(f, c_2, (25.359085660117678, 17.78529354637122)) → D_1
  44. Intersect(f, b_2, (8.314549691799938, -7.403901038585482)) → E_1
  45. Intersect(f, a_2, (2.9868060725339998, -2.982346512378994)) → F_1
  46. Intersect(f, t_1, (0.41291792669726235, 10.399494905323442)) → G_1
  47. Intersect(f_1, c_1) → J_1, K_1

AI 绘图提示语参考

画一个笛卡尔抛物线和圆的交点图,展示它们在坐标系中的相交情况。先画一个圆和抛物线,然后找到它们的交点。接着,从这些交点画出垂直于抛物线的直线,并标记这些直线的交点。最后,添加一些辅助线段和中点圆,以展示正交性和对称性。
以上提示语为根据原始绘图命令整理而来,仅供参考。