Example of Locus

Question

A variable plane which remains at a constant distance 3P from the origin cuts the coordinate axis at A, B, C. Show that the locus of the centroid of ∆ABC is   1/X2+1/Y2+1/Z2= 1/P2 . 

Answer 1

Let the equation of plane be x/a+y/b+z/c=1,  where a,b,c are intercepts of plane on x,y,z axis respectively.