A variable plane cutting coordinate axes in \( A, B, C \) is at a constant distance from the ori...

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A variable plane cutting coordinate axes in \( A, B, C \) is at a constant distance from the origin. Then the locus of centroid of the \( \triangle A B C \) is
(a) \( x^{-2}+y^{-2}+z^{-2}=16 \)
(b) \( x^{-2}+y^{-2}+z^{-2}=9 \)
(c) \( \frac{1}{9}\left\{\frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{z^{2}}\right\}^{-1}=0 \) (d) \( X+Y=0 \)
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