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一、问题如图1,设点P是椭圆E:x2/4+y2=1上的任意一点(异于左、右顶点A,B).(1)设椭圆E的右焦点为F,上顶点为C,求以F为圆心且与直线AC相切的圆的半径;(2)设直线PA,PB分别交直线l:x=10/3于点M、N,求证:PN⊥BM.
First, the problem is shown in Figure 1. Let the point P be any point on the ellipse E:x2/4+y2=1 (different from the left and right vertices A, B). (1) Set the right focus of the ellipse E to be F. The vertex is C. Find the radius of the circle centered on F and tangent to the straight line AC. (2) Set the straight line PA and PB to intersect the line l:x=10/3 at points M and N respectively. Verify that: PN⊥BM.