A variable plane at a distance of 1 unit from the origin cuts the coordinate axes at A, B and C. If the centroid D(x, y, z) of triangle ABC satisfies the relation 1x2+1y2+1z2=k  then the value of k is

Let the equation of the variable plane be  xa+yb+zc  which meets the axe s at A(a, 0, 0), B(0, D, 0) and C(0, 0, c).The centroid of  ∆ABC is a3,b3,c3 and it satisfies the relation   1x2+1y2+1z2=k,thus, 9a2+9b2+9c2=kor   1a2+1b2+1c2=k9----iAlso it is given that the distance of the plane  xa+yb+zc=1from (0,0,0) is 1 unit.Therefore 11a2+1b2+1c2=1 or 1a2+1b2+1c2=1From (i) and (ii), we get k9=1, i.e., k = 9