过两曲线f_1(x,Y)=0与f_2(x,y)=0交点的曲线方程f_1(x,y)+λf_2(x,y)=0在统编教材中已作习题提出,笔者以为这两曲线并集的曲线方程f_1(x,y)f_2(x,y)=0亦同样应引起重视。因为前者固可在两高次曲线的交族中找到所需要的曲线,而后者则可将两低次曲线合并为高次曲线。这些都是解析法处理问题时常用的变形技巧。平面上,我们经常研究一直线1:f(x,y)=0 The curve equation f_1(x,y)+λf_2(x,y)=0 at the intersection point of two curves f_1(x,Y)=0 and f_2(x,y)=0 has been put forward in the textbook, the author The curve equation f_1 (x, y) f_2 (x, y) = 0 for which the two curves are combined should also be taken seriously. Because the former can find the required curve in the intersection of two high-order curves, the latter can combine the two low-order curves into higher-order curves. These are commonly used deformation techniques when dealing with problems with analytics. On the plane, we often study the straight line 1:f(x,y)=0