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在平面解析几何教学中,动点的轨迹方程是教学的重点与难点.求轨迹方程不仅涉及到代数、几何,三角等多方面的知识,而且还要具备一定的分析综合能力.近几年的高考及数学竞赛,这类题目经常出现,而这类题变化繁多,学生感到难以对付,本文试就求轨迹方程的几种方法归纳整理如下:一 直接法直接设轨迹的动点坐标,以获得所求的轨迹方程.步骤:(1)适当选取坐标系;(2)设动点的坐标 P(x,y);(3)列出x,y的关系式;(4)化简.关键:列出x,y的关系式.例1.AB为半径a的圆的一条定直径,M为圆上任意一点,从A作直线AN,垂直于过M点的切线
In plane analytic geometry teaching, the trajectory equation of the moving point is the focus and difficulty of teaching. Finding the trajectory equation not only involves knowledge of algebra, geometry, triangle and other aspects, but also has a certain analytical comprehensive ability. In recent years In the college entrance examination and mathematics competitions, such topics often appear, and these kinds of questions have many changes, and students find it difficult to deal with them. This paper tries to find out several methods of seeking trajectory equations as follows: A direct method directly sets the coordinates of the moving points of the trajectory to obtain The trajectory equation to be sought. Steps: (1) properly select the coordinate system; (2) coordinate of the setpoint P(x,y); (3) list the relational expression of x,y; (4) simplify. : List the relation of x, y. Example 1. AB is a constant diameter of a circle with radius a, M is any point on the circle, A is a straight line from A, and a tangent is perpendicular to point M.