A variable plane which remains at q constant distance `3p` from the origin cut the coordinate axes at `A ,\ B ,\ Cdot` Show that the locus o the centroid of triangle `A B C` is `x^(-2)+y^(-2)+z^(-2)=p^(-2)dot`

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

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

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.

A sphere of constant radius k , passes through the origin and meets the axes at A ,Ba n d Cdot Prove that the centroid of triangle A B C lies on the sphere 9(x^2+y^2+z^2)=4k^2dot

A circle of radius 'r' passes through the origin O and cuts the axes at A and B,Locus of the centroid of triangle OAB is