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一、二曲线的和系定义1:在实数域内,设有二曲线 f_1(x、y)=0,f_2(x、y)=0,称曲线系mf_1(x、y)+nf_2(x、y)=0为曲线f_1、f_2的和系.m、n是不为0的实参数.令λ=n/m,则曲线f_1、f_2的和系可以写成: f_1(x、y)+λf_2(x、y)=0,当f_1=f_2时,规定λ≠—1。性质1:当二曲线f_1(x、y)=0与f_2(x、y)=0有公共点时,二曲线的和系f_1(x、y)+λf_2(x、y)=0为过f_1、f_2公共点的曲线系。性质2:除曲线f_1(x、y)=0与f_2(x、y)=0的公共点以外,二曲线的和系f_1(x、y)+λf_2(x、y)=0与曲线f_1或f_2没有其他的公共
The sum system of the first and second curves is defined as 1: In the real domain, there are two curves f_1 (x, y) = 0, f_2 (x, y) = 0, and the curve is mf_1 (x, y) + nf_2 (x, y) = 0 is the sum of the lines f_1, f_2 and .m, where n is a real parameter that is not 0. Let λ = n/m, then the sum of the curves f_1, f_2 can be written as: f_1(x, y) + λf_2 (x, y) = 0, when f_1 = f_2, specifies λ ≠ -1. Property 1: When the two curves f_1 (x, y) = 0 and f_2 (x, y) = 0 have common points, the sum of the two curves f_1 (x, y) + λf_2 (x, y) = 0 is The f_1, f_2 common point curve system. Property 2: In addition to the common point of the curves f_1 (x, y)=0 and f_2 (x, y)=0, the sum system of the two curves f_1 (x, y)+λf_2 (x, y)=0 and curve f_1 Or f_2 no other public