Four points lying on the rectangular hyperbola xy = c² are concyclic, and their coordinates are given by (c t1, c/t1), (c t2, c/t2), (c t3, c/t3), and (c t4, c/t4). Then

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Accepted Answer

t1 t2 t3 t4 = 1. Substituting (ct, c/t) into a general circle and multiplying by t^2 gives c^2 t^4 + 2gc t^3 + k t^2 + 2fc t + c^2 = 0. The product of the four roots is c^2/c^2 = 1, so t1 t2 t3 t4 = 1.

Four points lying on the rectangular hyperbola xy = c² are concyclic, and their coordinates are given by (c t1, c/t1), (c t2, c/t2), (c t3, c/t3), and (c t4, c/t4). Then

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