求二次曲线的弦的中点轨迹是中学解析几何中的一个难点,它包括求(一)平行弦的中点轨迹;(二)过二次曲线内(或外,或上)的一个定点(包括焦点)的直线截二次曲线所得弦的中点轨迹;(三)弦长为定值的动弦的中点轨迹。其中焦点弦的中点轨迹利用二次曲线的极坐标方程求解最为简便,其他类型的轨迹用直线的标准参数方程求解较为简便。 Finding the midpoint trajectory of the chord of the quadratic curve is a difficult point in middle school analytic geometry. It involves finding the midpoint trajectory of the (1) parallel chord; (2) a fixed point within (or outside, or above) the quadratic curve. The midpoint trajectory of the string resulting from the straight quadratic curve (including the focus); (c) The midpoint trajectory of the chord with a fixed chord length. The midpoint trajectory of the focal string is solved using the polar equation of the quadratic curve. The solution to other types of trajectories is simple and convenient with the standard parametric equation of the straight line.