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A variable chord of the circle x^(2) + ...

A variable chord of the circle ` x^(2) + y^(2) = 4` is drawn from the point P(3,5) meeting t he circle at the points A and B . A point Q is taken on this chord such that `2PQ = PA + PB `.The locus Q is

A

` x^(2) + y^(2) + 3x + 4y = 0 `

B

` x^(2) + y^(2) = 36`

C

` x^(2) + y^(2) = 16`

D

` x^(2) + y^(2) - 3x - 5y = 0 `

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The correct Answer is:
D
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