# The line x = y touches a circle at the point (1,1). If the circlealso passes through the point (1, - 3) , then its radius is : Option 1) 3 Option 2) $2\sqrt2$ Option 3) 2 Option 4) $3\sqrt2$

From tha family of circle and line circle touch the line $x-y=0$ at point (1,1)

$(x-1)^{2}+(y-1)^{2}+\lambda(x-y)=0$.................(1)

It passes through ( 1 , -3 )

$16 + \lambda (4)=0$

$\lambda=-4$

Put  $\lambda=-4$ in (1)

$(x-1)^{2}+(y-1)^{2}+(-4)(x-y)=0$

$=> x^{2}+y^{2}-6x+2y+2=0$

$r=\sqrt{g^{2}+f^{2}-c}$

$r=2\sqrt2$

$\therefore$ correct option is (2)

Option 1)

3

Option 2)

$2\sqrt2$

Option 3)

2

Option 4)

$3\sqrt2$

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