如图,在平面直角坐标系中,⊙P与x轴相切于原点O,平行于y轴的直线交⊙P于M,N两点.若点M的坐标是(2,-1),则点N的坐标是(  ) A.(2,-4) B.(2,-4.5) C.(2,-5) D.(2,-5.5)

问题描述:

如图,在平面直角坐标系中,⊙P与x轴相切于原点O,平行于y轴的直线交⊙P于M,N两点.若点M的坐标是(2,-1),则点N的坐标是(  )
A. (2,-4)
B. (2,-4.5)
C. (2,-5)
D. (2,-5.5)

过点M作MA⊥OP,垂足为A
设PM=x,PA=x-1,MA=2
则x2=(x-1)2+4,
解得x=

5
2

∵OP=PM=
5
2
,PA=
5
2
-1=
3
2

∴OP+PA=4,所以点N的坐标是(2,-4)
故选A.