Question

曲線f(x,y)=0關于直線x－y－2=0對稱的曲線方程是

A.f(y+2,x)=0                                                   B.f(x－2,y)=0

C.f(y+2,x－2)=0                                              D.f(y－2,x+2)=0

Answer 1

C

解析:

設M(x,y)為所求曲線上任一點，則它關于直線x－y－2=0的對稱點M′(x₀,y₀)在已知曲線f(x,y)=0上，即f(x₀,y₀)=0.

∵ M、M′關于直線l:x－y－2=0對稱,

∴MM′⊥l且MM′的中點在l上.

∴解得

又∵f(x₀,y₀)=0,∴f(y+2,x－2)=0.