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文献[1],[2],[3]均给出了2014年全国高中数学联赛江苏赛区复赛试题第一试第三题及其解答(且两者完全相同),笔者发现其解答有误,下面给出这道赛题的完整解答.赛题(2014年全国高中数学联赛江苏赛区复赛试题第一试第三题)已知动点A、B在椭圆x~2/8+y~2/4=1上,且线段AB的垂直平分线始终过点P(-1,0).(1)求线段AB中点M的轨迹方程;
Literature [1], [2], [3] gave the first test of the 2014 National Senior High School Mathematic Competition Jiangsu Division the first test of the third question and answer (and the two are exactly the same), I found that the answer is incorrect, The full answer to this question is given below: The question point (the third test of the first test of the 2014 National High School math match in Jiangsu Division) is that the moving points A and B are in the range of x ~ 2/8 + y ~ 2 / 4 = 1, and the vertical bisector of the line AB always passes P (-1,0). (1) Find the locus equation of the midpoint M of the line segment AB;