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在六年制重点中学高中数学课本《解析几何》P186.3中有这样一个习题:设x=t-t~2(t是参数),化普通方程x~2+2xy+y~2+2x-2y=0为参数方程。解这个习题,最后得两组参数方程: x+t-t~2 y=t~2+t’ x=t-t~2 y=t~2-3t+2 究竟这两组参数方程有什么关系?它们是否表示同一曲线?本文讨论如下。
In the six-year key middle school high school mathematics textbook “Analytic Geometry” P186.3, there is such an exercise: Let x = tt ~ 2 (t is a parameter), normalized equation x~2+2xy+y~2+2x-2y =0 is the parametric equation. To solve this problem, we finally get two sets of parameter equations: x+tt~2 y=t~2+t’ x=tt~2 y=t~2-3t+2 What is the relationship between these two sets of parametric equations? Representing the same curve? This article discusses the following.