Question

命題A:兩曲線F(x,y)=0和G(x,y)=0相交于點P(x₀,y₀);命題B:曲線F(x,y)+λG(x,y)=0(λ為常數(shù))過P(x₀,y₀),則A是B的_______________條件.

Answer 1

充分不必要?

解析:由條件,若兩曲線交于P(x₀,y₀),則有F(x₀,y₀)=0,及G(x₀,y₀)=0.?

故有F(x₀,y₀)+λG(x₀,y₀)=0,?

即F(x,y)+λG(x,y)=0,過P(x₀,y₀),即由A可推出B,反之則不可以.