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A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axis at A, B, C. Show that the locus of the centroid of triangle ABC is 1/x2 + 1/y2 + 1/z2 = 1/p2.

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Equation of plane cutting intercepts (say, a, b, c) on the axes is

x/a + y/b + z/c = 1. with A(a,0,0), B(0,b,0) and C(0,0,c) distance of this plane from origin is

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