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A circle with centre (3alpha, 3beta) an...

A circle with centre `(3alpha, 3beta)` and of variable radius cuts the rectangular hyperbola `x^(2)-y^(2)=9a^(2)` at the points `P, Q, S, R`. Prove that the locus of the centroid of triangle PQR is `(x-2alpha)^(2)-(y-2beta)^(2)=a^(2)`.

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