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If the circles x^2+y^2-16x-20y+164=r^2 a...

If the circles `x^2+y^2-16x-20y+164=r^2` and `(x-4)^2+(y-7)^2=36` intersect at two points then (a) `1ltrlt11` (b) `r=11` (c) `rgt11` (d) `0ltrlt1`

A

`r = 11`

B

`1 lt r lt 11`

C

`r lt 11`

D

`0 lt r lt 1`

Text Solution

Verified by Experts

The correct Answer is:
B
The circle
`(x-8)^(2)+(y-10)^(2)=r^(2)" or "(x-4)^(2)+(y-7)^(2)=(6)^(2)`
The intersect in two distinct points if w
`|r-6|lt5ltr+6`
`rArr" "|r-6| lt 5," "1ltrlt11`
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