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Two circle touch the x-axes and the line...

Two circle touch the x-axes and the line `y=mx` they meet at (9,6) and at one more point and the product of their radius is `117/2` then the value of m is

A

`2sqrt(2)`

B

`sqrt(2)`

C

`(1)/(sqrt(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A

Let the centre of `C_(1)` be (a,na)
`rArr (a-9)^(2) + (na-6)^(2) = (na)^(2)` (1)
Also, `m = (2n)/(1-n^(2))`
From (1), `a^(2) +117 - 18a - 12 na = 0`
`rArr a^(2) -a (18+12n) +117 = 0`
`rArr a_(1)a_(2) = 117`
`rArr r_(1)r_(2) = n^(2) a_(1)a xx 117 = (117)/(2)`
`rArr n^(2) = (1)/(2) :. m = 2sqrt(2)`
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