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1问题(2013年浙江六校)一个半径为2的球放在桌面上,桌面上的一点A1的正上方有一个光源A,AA1与球相切,AA1=6,球在桌面上的投影是一个椭圆,则这个椭圆的离心率等于()A.1/2B.2(1/2)/2C.2(1/2)/3D.3(1/2)/2本题近年来多次出现在各地高考模拟试卷中,初识本题,笔者有种“无可奈何花落去,似曾相识燕归来”的感觉!迫于首先要解决问题,用了一般性的方法进行了如下的尝试:2拙解解:如图2,过A,O两点的截面截球交底面于DE,AA1,AD与球切于C,C`,DE与A1A2交于F点,易知
1 Problem (2013 6th Zhejiang University) A ball of radius 2 is placed on the desktop with a light source A directly above a point A1 on the desktop. AA1 is tangent to the ball and AA1 = 6. The projection of the ball on the desktop is An ellipse, then the elliptical eccentricity is equal to () A.1 / 2B.2 (1/2) /2C.2 (1/2) /3D.3 (1/2) / 2 This problem has appeared many times in recent years In the college entrance examination simulation papers throughout the first acquaintance of the problem, I kind of “no choice to spend, deja vu return ” feeling! Forced to solve the problem first, with the general method of the following attempts: Solution: As shown in Fig. 2, the cross-section of the cross-section of A and O intersects at DE, AA1, AD and the ball cut at C, C ’, DE and A1A2 at point F,