A variable plane is at a constant distance `p` from the origin and meets the coordinate axes in `A , B , C` . Show that the locus of the centroid of the tehrahedron `O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot`

Explanation

`frac{{x}}{{a}}+frac{{y}}{{b}}+frac{{z}}{{c}}+=1 ldots (1) `


Since, the plane is at a distance of `p` from origin


`p=frac{1}{sqrt{frac{1}{a^{2}}+frac{1}{b^{2}}+frac{1}{c^{2}}}} `

`frac{1}{p^{2}}=frac{1}{a^{2}}+frac{1}{b^{2}}+frac{1}{c^{2}} ldots ldots(2)`



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