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The line x = y touches a circle at the ...

The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, -3). Then its radius is 0

A

`3sqrt(2)`

B

3

C

`2sqrt(2)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Family of circles touching the line y-x=0 at (1,1)
`(x-1)^(2) + (y-1)^(2) + lambda(y-x) =0`……..(i)
Since circle passes through (1,-3)
So, it must satisfy equation (i)
`0^(2) + 16 + lambda(-3-1) =0, lambda =4`
On putting the value of `lambda` in equation (i)
`(x-1)^(2) (y-1)^(2) + 4(y-x)=0`
`x^(2) -y^(2) - 6x +2y +2=0`
Hence, radius of the circle `=sqrt(9+1-2) = sqrt(8) = 2sqrt(2)`
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