文[1]得到了椭圆切线的一个优美性质(原文定理):性质如图1,如A,B分别是椭圆x~2/a~2+y~2/b~2=1(a>n>0)短轴(长轴)的两个端点,P为椭圆上的任意一点(不与A,B重合),直线PB,PA交长轴(短轴)所在直线于C,D,则椭圆在点P处的切线平分线段CD.文[1]还对这一类性质进行综合推广.在此基础上本文再作些补充推广.1推广至双曲线定理1若A,B分别是双曲线x~2/a~2-y~2/b~2=1实轴的两个端点,P为双曲线上的任意一点(不与A,B重合),直线PA,PB交虚轴所在直线于C,D两 In [1], a graceful property of the elliptic tangent is obtained. The properties are shown in Fig.1. For example, A and B are ellipses x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 > 0) both ends of the minor axis (major axis), P is any point on the ellipse (not coincident with A, B), and the straight line where the major axis (minor axis) The tangent line at point P bisects the line segment CD. [1] also generalizes this kind of property, on the basis of which some further generalizations are made.1 Generalization to Hyperbolic Theorem 1 If A and B are hyperbolic x 2 / a 2 y 2 / b 2 = 1 The two end points of the real axis P is any point on the hyperbola (not coincident with A and B) In C, D two