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Question

From the origin chords are drawn to the circle (x1)2+y2=1. The equation of the locus of the middle points of these chords is


A

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B

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C

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Solution

The correct option is C


The given circle is x2+y22x=0. Let (x1,y1) be the middle point of any chord of this circle, than its equation is S1=T.

or x21+y212x1=xx1+yy1(x+x1)

If it passes through (0,0), then

x21+y212x1=x1x21+y21x1=0

Hence the required locus of the given point (x1,y1) is x2+y2x=0


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