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A variable chord of the circle x^2+y^2=4...

A variable chord of the circle `x^2+y^2=4` is drawn from the point `P(3,5)` meeting the circle at the point `A` and `Bdot` A point `Q` is taken on the chord such that `2P Q=P A+P B` . The locus of `Q` is `x^2+y^2+3x+4y=0` `x^2+y^2=36` `x^2+y^2=16` `x^2+y^2-3x-5y=0`

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