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经研究发现,椭圆有如下的一个与切线有关的优美而简捷的性质.性质1若A1,A2为椭圆x2/a2+y2/b2=1(a>b>0)的左、右顶点,P为椭圆上任意一点(不同于A1,A2),直线PA1,PA2分别交直线l:x=t于点M,N,以点P为切点的切线交直线l于点Q,则Q为MN的中点.证明如图1(|t|>a时)和图2(|t| b> 0), P Is the ellipse on any point (different from A1, A2), the line PA1, PA2 were in line l: x = t at the point M, N, the point P as the tangent point tangent line l at point Q, Q is MN , We prove that P (x0, y0), x0 ≠ ± a, M (t, m) and N (t) are the same as those in Figure 1 (| t | t, n).