定理 F_1、F_2是椭圆 x~2/a~2+y~2/b~2=1(a>b>0)的两焦点,直线 l_1过长轴顶点 A_2且垂直于长轴,l_2为准线且交x轴于 H,B_1为短轴上的一个顶点,P、Q 分别为 l_1、l_2上的动点,且 A_2P、HQ 与 OB_1同向(图1),则当 PA_2=b,QH=ab/c 时,∠A_1QA_2,∠F_1PF_2各达到自己的最大值∠F_1B_1O.引理线段 AB 延长线与直线 l 交于 C 点,P 为 l 七的点,则当且仅当 PC~2=CA·AB 时,∠APB 达到最大(图2). The theorem F_1 and F_2 are the two focal points of an ellipse x 2 / a 2 + y 2 / b 2 = 1 (a> b> 0). The straight line l_1 is perpendicular to the long axis and vertex A_2, Line and the intersection of x-axis and H, B_1 is a vertex on the short axis, P and Q are the moving points on l_1 and l_2 respectively, and A_2P and HQ are the same direction as OB_1 (Fig.1). When PA_2 = b and QH = ab / c, ∠A_1QA_2, ∠F_1PF_2 each reach its maximum value ∠F_1B_1O. Least-line AB extension line and the line l intersect at point C, P is seven points, and if and only if PC ~ 2 = When CA · AB, ∠APB reached the maximum (Figure 2).