当a为任意实数时,直线(a-1)x-y+2a+1=0恒过的定点是(  ) A.(2,3) B.(-2,3) C.(1,-12) D.(-2,0)

问题描述:

当a为任意实数时,直线(a-1)x-y+2a+1=0恒过的定点是(  )
A. (2,3)
B. (-2,3)
C. (1,-

1
2

D. (-2,0)

当a为任意实数时,直线(a-1)x-y+2a+1=0恒过定点P,
则直线可化为(x+2)a+(-x-y+1)=0,
对于a为任意实数时,
此式恒成立有

x+2=0
−x−y+1=0

x=−2
y=3

故定点坐标是(-2,3).
故选B.