Question:
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 :
Correct Option: , 3
Solution:
Equation of circle can be written as $(\mathrm{x}-1)^{2}+(\mathrm{y}-1)^{2}+\lambda(\mathrm{x}-\mathrm{y})=0$
It passes through $(1,-3)$
$16+\lambda(4)=0 \Rightarrow \lambda=-4$
So $(x-1)^{2}+(y-1)^{2}-4(x-y)=0$
$\Rightarrow x^{2}+y^{2}-6 x+2 y+2=0$
$\Rightarrow r=2 \sqrt{2}$
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