本文从一道作业题出发,探讨了解决曲线交点问题的方法,得出判别式法是解决此类问题的通法.在学习平面解析几何中,最重要的是树立解析思想,用代数的方法解决几何问题,以及在代数运算过程中表达了怎么样的几何现象.例如两曲线交点问题,曲线C1:f(x,y)=0与曲线C2:g(x,y)=0有交点的充要条件是方程组f(x,y)=0,g(x,y)=⊙0有实数解.通常情况下,我们先将方程组消元转化为一元二次方程,再利用判别式法来讨论实数解的情况,这样的转化是否等价呢?刊物上不断有文章对曲线交点问题提出新的解决方法,而解决此类问题的通法为判 This paper starts from a homework question and explores the method to solve the intersection problem of the curve, and draws the discriminant method is the general method to solve such problems.In the study plane analytic geometry, the most important is to establish analytical thinking, algebraic method Such as the intersection of two curves, the intersection of C1: f (x, y) = 0 and curve C2: g (x, y) = 0 The condition is that the system of equations f (x, y) = 0, g (x, y) = ⊙0 has real solution. Usually, we first convert the elimination of equations into a quadratic equation, and then use the discriminant method To discuss the case of real number solutions, is such a transformation equivalent? Publications have articles on the intersection of the curve proposed a new solution, and the solution to such problems