Question

若点A(x₀,y₀)不在曲线f(x,y)=0上,则曲线f(x,y)+λf(x₀,y₀)=0(λ∈R且λ≠0)与曲线f(x,y)=0的交点个数为(    )

A.0                B.1                  C.无数个            D.以上都不对

Answer 1

A

解析：由已知f(x₀,y₀)≠0,设P(x₁,y₁)是f(x,y)=0上的点,则f(x₁,y₁)=0,但f(x₁,y₁)+λf(x₀,y₀)≠0,即P(x₁,y₁)不在曲线f(x,y)+λf(x₀,y₀)=0上.故选A.