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直线与圆锥曲线相交所得中点弦问题,是解析几何的重要内容之一,也是高考中经久不衰的热点.此类问题若用一般解法,不仅过程繁琐,而且运算量大又容易出错,而利用“点差法”解决这类问题,常常能起到化繁为简、出奇制胜的效果.本文采撷课本和近三年高考试卷中若干中点弦问题,从不同的视角加以审视归纳,分类例说“点差法”在解此类问题中的巧用,希望对大家有所帮助.一、斜率之积为定值的问题例1(2015年全国高考题)已知椭圆C:
The mid-point string problem caused by the intersection of a straight line and a conic curve is one of the important contents of analytic geometry and also an enduring hot spot in the college entrance examination. If the general solution is adopted for such a problem, not only is the process cumbersome but also the operation amount is large and error prone, The use of “spread ” to solve such problems, often can play simplistic, surprisingly winning effect.This text picks the textbook and the recent years college entrance examination papers in a number of mid-point string problem, from different perspectives to review induction, classification For example, “spread” in solving such problems in the clever use, I hope for everyone to help. First, the product of the slope of the value of the problem Example 1 (2015 National Entrance Examination) Known oval C: