平行于直线2x-y+1=0且与圆x2+y2=5相切的直线的方程是(  ) A.2x-y+5=0 B.x2-y-5=0 C.2x+y+5=0或2x+y-5=0 D.2x-y+5=0或2x-y-5=0

问题描述:

平行于直线2x-y+1=0且与圆x2+y2=5相切的直线的方程是(  )
A. 2x-y+5=0
B. x2-y-5=0
C. 2x+y+5=0或2x+y-5=0
D. 2x-y+5=0或2x-y-5=0

设圆切线为2x-y+m=0,
则圆心(0,0)到2x-y+m=0的距离d=

|m|
22+(−1)2
=r=
5
,即|m|=5,解得m=5或m=-5,
所以所求切线方程为2x-y+5=0或2x-y-5=0
故选D