六年制重点中学高中数学课本《解析几何》中有不少习题,若应用下述结论将使解法大大简化。定理设两条曲线的方程是f_1(x,y)=0与f_2(x,y)=0,P(x_o,y_o)是它们的交点。则方程为f_1(x,y)+λf_2(x,y)=0(λ是任意常数)的曲线也经过点P(x_o,y_o). 证明因为P(x_0,y_0)是f_1(x,y)=0 There are quite a few exercises in Analytic Geometry in the high school mathematics textbook for the six-year key middle school. If the following conclusion is applied, the solution will be greatly simplified. The theorem sets the equations of the two curves to be f_1(x,y)=0 and f_2(x,y)=0, and P(x_o,y_o) is their intersection point. The curve with the equation f_1(x,y)+λf_2(x,y)=0 (λ is an arbitrary constant) also passes the point P(x_o,y_o). Prove that P(x_0,y_0) is f_1(x,y) )=0