笔者发现椭圆和双曲线切线的一个新性质 ,并由此得到椭圆和双曲线切线的一种新颖作法 .定理 1　设 P为椭圆 x2a2 + y2b2 =1上任一点 ,过原点 O作焦半径 PF1的平行线交椭圆在 P点处的切线于 T,则 | OT| =a,且 TF2 ⊥PT.图 1　　　　　图 2证明　如图 1所示 ,延长 F1P,F2 T交于点 The author finds a new property of elliptic and hyperbolic tangent lines, and thus obtains a novel approach for elliptic and hyperbolic tangents. Theorem 1 Let P be an ellipse x2a2 + y2b2 =1 at any point, over the origin O for the parallel of PF1 The line tangent to the ellipse at point P is tangent to T, then | OT| = a, and TF2 ⊥ PT. Fig. 1 Fig. 2 prove that as shown in Fig. 1, extend F1P, F2 T intersect at the point