曲线和方程是解析几何中最重要的基本概念。如果某曲线上的点与某二元方程f(x,y)=0建立了如下对应关系: (1) 曲线上的点的坐标都是方程的解 (2) 以这个方程的解为坐标的点都是曲线上的点。那么,这个方程叫曲线的方程;这条曲线叫方程的曲线。教学时,习惯于用(1)来解题。对(2)却不太习惯,其实(2)在解题中也常可化难为易。下面通过几例说明。 [例1] P(a,b)是定直线上x+y=1的定点,且a≠b,Q(c,d)是定直线上的动点,求证,存在实 Curves and equations are the most important basic concepts in analytical geometry. If the point on a curve and a certain binary equation f(x, y) = 0 establish the following correspondence: (1) the coordinates of the points on the curve are all solutions of the equation (2) using the solutions of this equation as coordinates Points are points on the curve. Then, this equation is called the equation of the curve; this curve is called the curve of the equation. When teaching, he is used to solving problems with (1). (2) is not quite accustomed to it. In fact, (2) is often difficult to solve in solving problems. Here are a few examples. [Example 1] P(a, b) is a fixed point where x + y = 1 on a fixed line, and a≠b, Q(c, d) is a moving point on a straight line, verification, existence