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Prove that the locus of the mid-points o...

Prove that the locus of the mid-points of chords of length 2d unit of the hyperbola `xy=c^(2)` is `(x^(2)+y^(2))(xy-c^(2))=d^(2)xy.`

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Prove that the locus of the mid-points of chords of length 2d units of the hyperbola xy=c^2 is (x^2+y^2)(xy-c^2)=d^2xy

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