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)
答
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
得
,
x=−2 y=3
故定点坐标是(-2,3).
故选B.