A variable plane at a distance of 1 unit from the origin cuts the co-ordinate axes at \( A, B \)...

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A variable plane at a distance of 1 unit from the origin cuts the co-ordinate axes at \( A, B \) and \( C \). If the centroid \( D(x, y, z) \) of triangle \( A B C \) satisfies the relation \( \frac{1}{x^{2}}+\frac{1}{y^{2}}+\frac{1}{z^{2}}=k \), then the value of \( k \) is the value of \( k \) is
(a) 3
(b) 1
(c) \( 1 / 3 \)
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