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问题设点Q是双曲线x2-y2=1上任意一点,F1、F2分别为其左、右焦点,过F1作∠F1QF2平分线的垂线,垂足为N,求点N的轨迹方程.这是近期高三测试卷中的一个问题,标准答案的错解引起师生的激烈讨论,现整理成文,希望对大家有所帮助.1错解呈现分析本题主要考察学生对双曲线、圆的定义的理解,体会平面几何在解析几何中“巧用定义”、“减少计算量”的作用等.
Problem set point Q is any point on the hyperbola x2-y2 = 1, F1, F2 are its left and right focus, respectively, F1 for ∠ F1QF2 bisector of the vertical line, the foot is N, and find the point N trajectory equation. This is the recent high school test volume in a question, the standard answer to the wrong teachers and students led to intense discussion, is now organized and written, I hope for everyone to help .1 misinterpretation presented analysis of the problem mainly examine the students of hyperbolic, the definition of a circle Understand the understanding of flat geometry in analytic geometry “clever use of definition ”, “reduce the amount of computation ” role and so on.