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某些解析几何题,题设条件之间蕴含逻辑矛盾,应是无解的,可是我们运用一些“常规”的解题方法,往往导出有解的结论;反之,本来有解的问题,却作出无解的判断。诸如此类的错误,不仅在学生作业中出现,而且散见于书刊一些作者的文章之中,因此,本文不得不为之一说。一、死套解题方法、技巧造成误判。例1 求过直线x+2y+1=0与圆x~2+y~2-2x-4y+1=0的交点,且过点(1,-2)的圆的方程。
Some analytical geometrical problems and logical conditions that contain logical contradictions between the questions are supposed to be non-existent. However, we use some “conventional” methods to solve problems and often derive solutions. On the other hand, problems that are originally solved have been made. No solution. Errors such as these appear not only in student assignments, but also in the articles of authors of books and periodicals. Therefore, this article has to be one of them. One, deadlock problem-solving methods, skills cause misjudgment. Example 1 Find the equation of the circle where the line x+2y+1=0 and circle x~2+y~2-2x-4y+1=0 intersect and the point (1,-2) crosses.