If a variable plane forms a tetrahedron of constant volume `64k^3` with the co-ordinate planes, then the locus of the centroid of the tetrahedron is:

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C. Show that the locus of the centroid of the tetrahedron OABC is (1)/(x^2)+(1)/(y^2)+(1)/(z^2)=(16)/(p^2) .

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C , show that the locus of the centroid of the tetrahedron OABC os 1/x^2+1/y^2+1/z^2= 16/p^2

A variable line is at constant distance p from the origin and meets the co-ordinate axes in A, B. Show that the locus of the centroid of the triangleOAB is x^(-2)+y^(-2)=9p^(-2)

a variable plane which is at a constant distance 3p from the origin O cuts the axes at A,B,C. Show that the locus of the centroid of the triangle ABC is x^(-2)+y^(-2)+z^(-2)=p^(-2) .

If a circle of constant radius 3K passes through the origin and meets the axes at A&B.the locus of the centroid of triangleOAB is

A variable plane which is at a constant distance 3p from origin cuts the coordinate axes at A,B,C respectively. Show that locus of the centroid of the triangleABC is 1/x^2+1/y^2+1/z^2= 1/p^2 .

A sphere of constant radius 2k passes through the origin and meets the axes in A ,B ,a n dCdot The locus of a centroid of the tetrahedron O A B C is a. x^2+y^2+z^2=4k^2 b. x^2+y^2+z^2=k^2 c. 2(x^2+y^2+z)^2=k^2 d. none of these

A variable plane passes through a fixed point (a ,b ,c) and cuts the coordinate axes at points A ,B ,a n dCdot Show that locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

A variable plane which is at a constant distance 3p from the origin O cuts the axes at L,M and N.Show that the locus of the points of intersection of the planes through L,M,N drwon parallel to the coordinate planes is 9(x^(-2)+y^(-2)+z^(-2))=p^(-2) .

If V be the volume of a tetrahedron and V ' be the volume of another tetrahedran formed by the centroids of faces of the previous tetrahedron and V=K V^(prime),t h e nK is equal to a. 9 b. 12 c. 27 d. 81