定理 1　设椭圆的一个焦点为F ,直线l与过椭圆长轴的端点A′ ,A的切线相交于M′ ,M ,则1)FM′·FM =0 直线l与椭圆相切 ;2 )FM′·FM 0 直线l与椭圆相离 ;3)FM′·FM 0 直线l与椭圆相交 .证　设椭圆方程 x2a2 +y2b2 =1(a ) ,F(c,0 ) ,A′(-a ,0 ) ,A(a ,0 ) .直线l:y =k Theorem 1 Let one focus of the ellipse be F, and the line l intersects with the tangent of the endpoint A’ of the long axis of the ellipse, A, in M′, M, then 1) FM′·FM =0 The line l is tangent to the ellipse; 2) FM’·FM 0 The line l is away from the ellipse; 3) FM’·FM 0 The line l intersects with the ellipse. It is proved that the elliptic equation x2a2 +y2b2 = 1(a), F(c,0), A’(-a ,0 ),A(a ,0 ) .Line l:y =k