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
答
设圆切线为2x-y+m=0,
则圆心(0,0)到2x-y+m=0的距离d=
=r=|m|
22+(−1)2
,即|m|=5,解得m=5或m=-5,
5
所以所求切线方程为2x-y+5=0或2x-y-5=0
故选D