定理　设Ｐ为圆锥曲线Ｅ上的任一点 ,ｌ为过点Ｐ的切线 ,ＰＡ ,ＰＢ为倾斜角互补的动弦 ,则(Ⅰ )直线ＡＢ与ｌ的倾斜角也互补 ;(Ⅱ )线段ＡＢ中点的轨迹是与原曲线具有相同离心率的圆锥曲线 (当原曲线为圆时 ,ＡＢ中点的轨迹亦是圆 ) .证明　①当圆锥曲线为椭圆、圆或双曲线时 Theorem Let P be any point on conic curve E, l be the tangent to the point P, PA, PB be the complement of the incline angle, then (I) the inclination angles of lines AB and l are also complementary; (II) Line AB The midpoint trajectory is a conic curve with the same eccentricity as the original curve (when the original curve is a circle, the trajectory of the AB midpoint is also a circle). Proof 1 When the conic curve is an ellipse, circle, or hyperbola