The coordinates of the center of a circle, whose radius is P 2 unit...

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The coordinates of the center of a circle, whose radius is
P 2 unit and which touches the line pair \( x^{2}-y^{2}-2 x+1=0 \), are
(1) \( (4,0) \)
(2) \( (1+2 \sqrt{2}, 0) \)
(3) \( (4,1) \)
(4) \( (1,2 \sqrt{2}) \)
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