A variable plane passes through a fixed point \( (a, b, c) \) and m...

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A variable plane passes through a fixed point \( (a, b, c) \) and meets the co-ordinate axes in A, B, C. Show that the locus of the point common to the planes through \( \mathrm{A}, \mathrm{B}, \mathrm{C} \) parallel to the co-ordinate planes is \( \frac{a}{x}+\frac{b}{y}+\frac{c}{z}=1 \).
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