(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is :
`(1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2))` .
(ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is :
`(1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).`