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

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

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 tetrahedron O A B C is x^(-2)+y^(-2)+z^(-2)=16p^(-2)

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 O A B Ci sx^(-2)+y^(-2)+z^(-2)=16p^(-2)dot

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 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, 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 :

If the plane x/2+y/3+z/4=1 cuts the coordinate axes in A, B,C, then the area of triangle ABC is

A circle of constant radius 3k passes through (0,0) and cuts the axes in A and B then the locus of centroid of triangle OAB is

A variable plane at constant distance p form the origin meets the coordinate axes at P,Q, and R. Find the locus of the point of intersection of planes drawn through P,Q, r and parallel to the coordinate planes.

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 eh locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.