A variable plane is at a constant distance 3p from the origin and meets the coordinates axes in A,B and C if the centroid of `triangle ABC` is `(alpha,beta,gamma )` then show that `alpha^(-2)+beta^(-2)+gamma^(-2)=p^(-2)`

A plane a constant distance p from the origin meets the coordinate axes in A, B, C. Locus of the centroid of the triangle ABC 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)

Find the equation of a plane which meets the axes in A,B and C, given that the centroid of the triangle ABC is the point (alpha,beta,gamma)

(i) A variable plane, which remains at a constant distance '3p' from the origin cuts the co-ordinate axes at A, B, C. Show that the locus of the centroid of the triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (1)/(p^(2)) . (ii) A variable is at a constant distance 'p' from the origin and meets the axes in A, B, C respectively, then show that locus of the centroid of th triangle ABC is : (1)/(x^(2)) + (1)/(y^(2)) + (1)/(z^(2)) = (9)/(p^(2)).

A plane meets the coordinates axis in A, B, C such that the centroid of the triangle ABC is the point (alpha, beta, gamma) . Find the equation of plane in intercept form.

The equation of the plane which makes with coordinate axes, a triangle witih centroid (alpha,beta,gamma) is given by