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The equation of the locus of the mid-poi...

The equation of the locus of the mid-points of chords of the circle `4x^(2) + 4y^(2) -12x + 4y + 1 = 0` that substend an angle `(2pi)/(3)` at its centre, is

A

`16x^(2) + 16y^(2) -48x + 16y + 31 = 0`

B

`16x^(2) + 16y^(2) + 48x + 48y + 31 = 0`

C

`16x^(2) - 16y^(2) + 48x + 48y + 31 = 0`

D

`16x^(2) - 16y^(2) - 48x + 16y - 31 = 0`

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The correct Answer is:
A
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