圆C1:x2+y2+2x+8y-8=0与圆C2:x2+y2-4x-4y-1=0的位置关系是(  )A.外离B.外切C.相交D.内

2025-05-08 20:27:52
推荐回答(1个)
回答1:

∵圆C1:x2+y2+2x+8y-8=0的圆心C1(-1,-4),
半径r1=

1
2
4+64+32
=5,
圆C2:x2+y2-4x-4y-1=0的圆心C2(2,2),
半径r2=
1
2
16+16+4
=3,
∴|C1C2|=
((2+1)2+(2+4)2
=3
5
,|r1-r2|=2,r1+r2=8 
∵|r1-r2|<|C1C2|<r1+r2
∴圆C1与圆C2相交.
故选C.