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将曲线的普通方程按照所给的条件化为参数方程,有时会出现两组解。是应该舍去其中的一组,还是两组解都应该保留?现行课本对这个问题未作任何说明。目前许多学生和少数教师在遇到有两组解时,总是习惯地舍去其中一组,殊不知这样做有时出现了错误。那么在什么情况下应该舍去其中一组解,舍去哪一组解?在什么情况下又不能舍去其中任何一组解呢?笔者谈点个人的粗浅看法。一、在两组解中,如果(A)组解所对应的点集是(B)组解所对应的点集的真子集,这时就该舍去(A)组篇。例1、设y=tx,化曲线方程x~2+2xy+y~2+2x-2y=0为参数方程。解:将y=tx代入所给的方程,整理得 x〔(t+1)~2x+2(1-t)〕=O
The ordinary equation of the curve is converted into a parametric equation according to the given conditions. Sometimes two sets of solutions appear. Is it a group that should be abandoned, or should the two groups of solutions be retained? The current textbook does not provide any explanation on this issue. At present, many students and a small number of teachers are always accustomed to giving up one set when they encounter two sets of solutions. They do not know that mistakes have sometimes occurred. Under what circumstances should one be left out of the group of solutions, which group of solutions should be discarded? Under what circumstances can it not be discarded from any one group of solutions? The author talks about the individual’s superficial views. First, in the two sets of solutions, if the set of points corresponding to the (A) group solution is the true subset of the set of points corresponding to the (B) group solution, then the (A) set of articles should be discarded. Example 1 Let y = tx, and the chemical curve equation x~2+2xy+y~2+2x-2y=0 is a parametric equation. Solution: Substitute y=tx into the given equation and sort it to x[(t+1)~2x+2(1-t)]=O