A variable plane intersects the co- ordinate axes at a distance `p` from `O(0,0,0)` .Then the locus of the centroid of the tetrahedron OABC is.....

A variable plane cutting coordinate axes in A, B, C is at a constant distance from the origin. Then the locus of centroid of the triangleABC is

A variable line intersects the co-ordinate axes at A and B and passes through a fixed point (a,b). then the locus of the vertex C of the rectangle OACB where O is the origin is

A variable straight line passes through a fixed point (a, b) intersecting the co-ordinates axes at A & B. If 'O' is the origin, then the locus of the centroid of the triangle OAB is (A) bx+ ay-3xy=0 (B) bx+ay-2xy=0 (C) ax+by-3xy=0 (D) ax+by-2xy=0.

If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A,B anc C, then the locus of the centroid of Delta ABC is :

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

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,C .Show that the locus of the centroid of the tehrahedron OABCisx^(-2)+y^(-2)+z^(-2)=16p^(-2)

A variable plane which remains at a constant distance p from the origin cuts the coordinate axes in A, B, C. The locus of the centroid of the tetrahedron OABC is x^(2)y^(2)+y^(2)z^(2)+z^(2)x^(2)=(k)/(p^(2))x^(2)y^(2)z^(2), then root(5)(2k) is

A variable plane forms a tetrahedron of constant volume 64k^3 with the coordinate planes and the origin, then locus of the centroid of the tetrahedron is