From origin, chords are drawn to the circle $x^{2} + y^{2} - 2 y = 0$ .The locus of the middle points of these chords is

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Solution

The correct option is A

$T = S_{1} i . e x x_{1} + y y_{1} - (y + y_{1}) = x_{1}^{2} + y_{1}^{2} - 2 y_{1}$
Passes through (0,0)
$∴ x^{2} + y^{2} - y = 0$

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