椭圆垂直切线交点的轨迹——蒙日圆（准圆）
2019-11-14 07:11
本范例演示椭圆的一个经典几何性质：从椭圆外一点作椭圆的两条互相垂直的切线，当切点变化时，这些交点的轨迹构成一个圆，称为蒙日圆（Monge Circle）或准圆（Director Circle）。对于标准椭圆 x²/a² + y²/b² = 1，其蒙日圆的方程为 x² + y² = a² + b²，即以椭圆中心为圆心、半径为 √(a²+b²) 的圆。通过 GeoGebra 动态构造，用户可以拖动切点观察垂直切线交点的运动轨迹，直观验证这一优美的圆锥曲线性质。涉及椭圆、切线、正交线、轨迹等核心概念。
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