If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of ΔABC is

Let the plane equation be
ax+by+cz+d=0
Distance of the plane from origin is 3, ∴d√a2+b2+c2=3
i.e. d2=9(a2+b2+c2) .. (1)
Now, the plane would intersect the x-axis at A(−da,0,0), y-axis at B(0,−db,0) and z-axis at C(0,0,−dc)
The centroid of this triangle would have the co-ordinates (−d3a,−d3b,−d3c)
Let h=−d3a, k=−d3b, l=−d3c
Using equation (1), we can write
19=19h2+19k2+19l2
→1=1h2+1k2+1l2