The locus of the mid-points of the chords of the circle which pass through the origin is
Let be the coordinates of the mid point.
Equation of the chord whose mid point is is
This chord passes through the origin
Hence
Hence the required locus is .
Alternative:
If is the slope of the chord, then
If is the slope of the perpendicular to the chord then is the centre of the given circle. But
Hence the required locus is .
Hence (B) is the correct answer.
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