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From the origin, chords are drawn to the...

From the origin, chords are drawn to the circle `(x-1)^2 + y^2 = 1`. The equation of the locus of the mid-points of these chords is circle with radius

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For the equation of circle `x^(2)+y^(2)-2x =0`. Let the mid-point of chords be (h,k).
`therefore` Equation of chord bisected at the point is `S_(1) = T`.
`therefore h^(2)+k^(2)-2h=xh+yk-(x+h)` which passes through (0,0).
`rArr h^(2)+k^(2)-2h=-h`
lt brgt `therefore` The required locus of a chord is `x^(2)+y^(2)-x=0`
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