过点(2,1)并与两坐标轴都相切的圆的方程是(  ) A.(x-1)2+(y-1)2=1 B.(x-1)2+(y-1)2=1或(x-5)2+(y-5)2=5 C.(x-1)2+(y-1)2=1或(x-5)2+(y-5)2=25 D.(x-5

问题描述:

过点(2,1)并与两坐标轴都相切的圆的方程是(  )
A. (x-1)2+(y-1)2=1
B. (x-1)2+(y-1)2=1或(x-5)2+(y-5)2=5
C. (x-1)2+(y-1)2=1或(x-5)2+(y-5)2=25
D. (x-5)2+(y-5)2=5

∵圆与两坐标轴都相切
∴设圆方程为﹙x-a﹚2+﹙y-a﹚2=a2
(2,1)代入,得:
﹙2-a﹚2+﹙1-a﹚2=a2
﹙a-5﹚×﹙a-1﹚=0
a=5或1
﹙x-5﹚2+﹙y-5﹚2=25
﹙x-1﹚2+﹙y-1﹚2=1.
故选:C.