Let A= (a, 0,0), B = (0, b, 0), C = (0,0, c), then equation of the plane is
++ = 1
Its distance from the origin,
++ =
... (i)
If (x, y, z) be centroid of δ ABC, then
x =
, y =
, z =
... (ii)
Eliminating a,b,c from (i) and (ii) required locus is
x−2+y−2+z−2 =
9p−2