论文部分内容阅读
性质1如图1,椭圆E:(x~2)/(a~2)+(y~2)/(b~2)=1(a>b>0)的左(右)焦点为F,在x轴上F的右(左)侧有一点A,以FA为直径作圆C与椭圆E在x轴上方部分交于M、N两点,则(|FM|+|FN|)/|FA|=1/e(其中e为椭圆的离心率).
Property 1 As shown in Figure 1, the left (right) focus of the ellipse E: (x ~ 2) / (a ~ 2) + (y ~ 2) / (b ~ 2) = 1 (a> b> 0) On the x-axis, there is a point A on the right (left) side of the F, a circle C with the diameter of FA, and a portion of the ellipse E intersecting the ellipse E at two points M and N above the x-axis, then (| FM | + | FN |) / | FA | = 1 / e (where e is the elliptical eccentricity).