If a variable plane cuts the coordinate axes in \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \...

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If a variable plane cuts the coordinate axes in \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) and is at a constant distance \( \mathrm{p} \) from the origin, if the locus of the centroid of the tetrahedron \( \mathrm{OABC} \) is \( x^{-2}+y^{-2}+z^{-2} \) \( =\lambda p^{-2} \), then \( \lambda \) is
(a) 4
(b) 32
(c) 16
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