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A point P moves so that three mutually p...

A point P moves so that three mutually perpendicular lines PA, PB, PC may be drawn cutting the axes OX, OY, OZ, at A, B,C and the volume of tetrahedron OABC is constant and equal to `k^3/6`. Prove that P lies on the surface `(x^2+y^2+z^2)^3 = 8 k^3 xyz`

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