The locus of the center of the circle touching the line \( \mathrm{...

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The locus of the center of the circle touching the line
\( \mathrm{P} \) \( 2 x-y=1 \) at \( (1,1) \) is

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(1) \( x+3 y=2 \)
(2) \( x+2 y=3 \)
(3) \( x+y=2 \)
(4) none of these
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