A variable plane passes through a fixed point \( (1,-2,3) \) and meets the co-ordinate axes in \...

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A variable plane passes through a fixed point \( (1,-2,3) \) and meets the co-ordinate axes in \( A, B, C \). The locus of the point of intersection of the planes through \( A, B, C \) parallel to the co-ordinate planes is the surface
(a) \( x y-\frac{1}{2} y z+\frac{1}{3} z x=6 \)
(b) \( y z-2 z x+3 x y=x y z \)
(c) \( x y-2 y z+3 z x=3 x y z \)
(d) None of these
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