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在高中教学第二册《极坐标》一节中,有一道习题:长为2a的线段,其端点在两个直角坐标轴上滑动,从原点作这个线段的垂线,垂足为M,求点M的轨迹的极坐标方程(ox为极轴),再化为直角坐标方程。(189页第12题)这一道习题的解答,在供教师教学使用的参考书上,写得比较含糊,有的地方尚不够完整,现把它摘录在下面:解如图一,设AB(=2a)的端点A、B分别在x轴和y轴上滑动。先考虑AB在第一象限的情况。设点M为适合条件之点,
In the high school teaching second volume “polar coordinates” section, there is a problem: the length of 2a line segment, the end point in two Cartesian coordinate axis, from the origin for the vertical line, the foot of M, seeking Point M's trajectory polar equation (ox polar axis), re-into Cartesian coordinates equation. (P. 189, p. 12) The answer to this question is more vaguely written on the reference books for teachers' teaching and is not yet complete enough in some places. = 2a) endpoints A, B slide on the x-axis and the y-axis, respectively. First consider AB in the first quadrant. Set point M is suitable for the point,