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If the two circles (x+1)^2+(y-3)=r^2 and...

If the two circles `(x+1)^2+(y-3)=r^2 and x^2+y^2-8x+2y+8=0` intersect in two distinct point,then

A

`2ltrlt8`

B

`rlt2`

C

r = 2

D

`r gt 2`

Text Solution

Verified by Experts

The correct Answer is:
A
As, the two circle intersect in two distinct points.
`rArr " Distance between centre lies between " |r_(1)-r_(2)| and |r_(1)+r_(2)|`.
i.e. `|r-3|ltsqrt((4-1)^(2)+(-1-3)^(2))lt|r+3|`
`rArr |r-3|lt5lt|r+3|rArrlt8 or rgt2`
`therefore 2ltrlt8`
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