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我们知道,圆锥曲线是高考考查的重要内容之一,而圆锥曲线中的最值问题更是无处不在.在很多教学参考书中,我们都会见到这样的类似问题:已知椭圆C的方程为1x62+1y22=1,F1、F2是它的左、右两个焦点,点A的坐标为(3,1),试在椭圆上求一点P,(1)使得|PA|+|PF2|最小;(2)使得|PA|+2|PF2|
We know that the conical curve is one of the important contents of the college entrance examination. The problem of the maximum value in the conic curve is even more ubiquitous. We will see similar problems in many teaching reference books: The equation of the ellipse C is known. For 1x62+1y22=1, F1 and F2 are its left and right two focal points. The coordinate of point A is (3, 1). Try to find a point P on the ellipse (1) so that |PA|+|PF2| Min; (2) makes |PA|+2|PF2|