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Help me understand! 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 :

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 :

  • Option 1)

    3

  • Option 2)

    2\sqrt2

  • Option 3)

    2

  • Option 4)

    3\sqrt2

 
Answers (1)
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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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