A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron \[OABC\] is

\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\]

\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-2}}\]

\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\]

\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16\]

A variable plane is at a constant distance p from the origin and meets

1.	A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron \[OABC\] is
A.	\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-2}}\]
B.	\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\]
C.	\[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16\]
D.	None of these
Answer» B. \[{{x}^{-2}}+{{y}^{-2}}+{{z}^{-2}}=16{{p}^{-1}}\]

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A variable plane is at a constant distance p from the origin and meets the axes in A, B and C. The locus of the centroid of the tetrahedron \[OABC\] is

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