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全国通用教材高中数学第二册的教学参考书中,对课本中“化极坐标p=5tgθ为直角坐标方程”一题(P_(188))给出的答案是:x·(x~2+y~2)~(1/2)=5y (P_(217))其实这个答案是错误的。因为方程x·(x~2+y~2)~(1/2)=5y所表示的曲线是:仅在第一、三象限内、过原点的曲线;(∵xy≥0)而原极坐标方程所表示的曲线却是可分布在四个象限、过原点的曲线。
In the teaching reference book of the second-grade mathematics textbook for high school mathematics in the National General Teaching Materials, the answer given in the textbook “The polar coordinate p=5tgθ is a Cartesian coordinate equation” (P_(188)) is: x·(x~2+) y~2)~(1/2)=5y (P_(217)) Actually this answer is wrong. Since the equation represented by the equation x(x~2+y~2)~(1/2)=5y is: only in the first and third quadrants, the curve through the origin; (∵xy≥0) and the original The curve represented by the coordinate equation is a curve that can be distributed in the four quadrants and over the origin.