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

Options

A. `2sqrt(2)`
B. `sqrt(2)`
C. `(1)/(sqrt(2))`
D. none of these

Answer

A

Explanation

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)`