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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

`3sqrt2`

B

`2sqrt2`

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
Since,the equation of family of circles touching line
L=0 a t their point of contact `(x_(1),y_(1))` " is " `(x-x_(1))^(2) +(y-y_(1))^(2)+lambdaL=0, " where " Lambda in R`.
`therefore` Equation of circle, touches the x= y at point (1, 1) is
`(x-1)^(2)+(y-1)^(2)+lambda(x-y)=0`
`rArr x^(2)+y^(2)+(lambda-2)x+(-lambda-2)y+2=0" "...(i)`
` therefore` CIrcle(i) passes through point (1, -3).
`therefore 1 + 9 +(lambda-2)+3(lambda+2)+2=0`
`rArr 4lambda + 16 = 0`
`rArr lambda = - 4`
So, equation of circle (i) at `lambda =-4` , is
`x^(2)+y^(2)-6x+2y+2=0`
Now, radius of the circle `=sqrt(9+1-2)=2sqrt2`.
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