绘制双曲线 by Jennifer Silverman
几何画板及绘图内容加载中,请稍等……
这是一个让学生了解双曲线如何构造的动态演示。通过使用GeoGebra命令,如Circle, Intersect, Rotate, Hyperbola等,学生可以直观地看到双曲线的形成过程。该范例适合高中数学教学,特别是解析几何和函数图像的学习。
GeoGebra 命令及参数
Circle(A_2, w) → cCircle(A_2, h) → dLine(A_2, xAxis) → eIntersect(c, e, 2) → B_2Rotate(B_2, α, A_2) → BTangent(B, c) → f,Line(B, A_2) → gIntersect(c, g, 2) → ATangent(A, c) → h_2,Circle(A, h) → kCircle(A, Radius[c]) → pCircle(B, Radius[d]) → qCircle(A, w) → rCircle(B, h) → sIntersect(r, s, 1) → IHyperbola(A, B, I) → tPoint(t) → DIntersect(t, e, 2) → EOrthogonalLine(E, e) → iIntersect(t, e, 1) → FOrthogonalLine(F, e) → jDistance(E, F) → distanceEFCircle(A_2, Segment[A_2, B]) → c_1Intersect(c_1, j, 1) → GOrthogonalLine(G, j) → lIntersect(c_1, j, 2) → HOrthogonalLine(H, j) → mIntersect(c_1, i, 1) → JIntersect(c_1, i, 2) → KPolygon(H, G, J, K) → poly1, h_1, g_1, j_1, k_1Line(J, H) → nLine(G, K) → a_1Segment(D, A) → s_1Segment(D, B) → s_2Segment(A_2, F) → aDistance(E, F) → a_2OrthogonalLine(A_2, a) → b_2Intersect(g_1, b_2) → LSegment(A_2, L) → bCircle(A_1, g_2) → h_3Circle(B_1, e_1) → k_2Intersect(h_3, k_2, 1) → C_1Ellipse(A_1, B_1, C_1) → p_1Line(A_1, B_1) → i_1Point(p_1) → B'_1Segment(A_1, B'_1) → j_2Segment(B_1, B'_1) → l_1Segment(A_1, B_1) → a_3Midpoint(a_3) → G_1OrthogonalLine(G_1, a_3) → b_3Intersect(p_1, b_3) → F_1, E_1Line(A_1, B_1) → c_2Intersect(p_1, c_2) → C_2, D_1Distance(G_1, D_1) → distanceGD_1Distance(G_1, E_1) → distanceGE_1Segment(G_1, E_1) → b_4Segment(G_1, D_1) → a_4
AI 绘图提示语参考
绘制一个双曲线,通过点A和B,它们分别位于直线e的两侧。首先画出两个圆c和d,然后通过旋转和交点找到双曲线的焦点I。接着使用A、B和I构造双曲线t,并在e上找到双曲线的两个顶点D和E。通过E和F的垂直线找到双曲线的渐近线i和j,最后确定双曲线的形状。
以上提示语为根据原始绘图命令整理而来,仅供参考。