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A variable plane cuts the co-ordinate axes in A, B, C and is of constant distance 3p from the origin. Find the locus

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A variable plane cuts the co-ordinate axes in A, B, C and is of constant distance 3p from the origin. Find the locus of the centroid of the triangle ABC.

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Let the equation of the plane be 

It is given that, 

OM = 3p

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