Circle \( x^{2}+y^{2}-2 x+\lambda x-1=0 \) passes through two fixed points, co-ordinates of thes...

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Circle \( x^{2}+y^{2}-2 x+\lambda x-1=0 \) passes through two fixed points, co-ordinates of these points are
(A) \( (0, \pm 1) \)
(B) \( (\pm 1,0) \)
(C) \( (0,1) \) and \( (0,2) \)
(D) \( (0,-1) \) and \( (0,-2) \)
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