From the origin chords are drawn to the circle (x - 1)2 + y2 = 1. The equation of the locus of the middle points of these chords is

1
x2 + y2 - 3x = 0
2
x2 + y2 - 3y = 0
3
x2 + y2 - x = 0
4
x2 + y2 - y = 0

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