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 constant radius 2r passes through the origin and meets the axes in 'P' and 'Q' Locus of the centroid of the trianglePOQ is :

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 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

If a circle of constant radius 3k passes through the origin O and meets the coordinate axes at Aa n dB , then the locus of the centroud of triangle O A B is (a) x^2+y^2=(2k)^2 (b) x^2+y^2=(3k)^2 (c) x^2+y^2=(4k)^2 (d) x^2+y^2=(6k)^2

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 circle passes through origin and meets the axes at A and B so that (2,3) lies on bar(AB) then the locus of centroid of DeltaOAB is

A variable line through the point P(2,1) meets the axes at A an d B . Find the locus of the centroid of triangle O A B (where O is the origin).

A circle of constant radius r passes through the origin O, and cuts the axes at A and B. The locus of the foots the perpendicular from O to AB is (x^(2) + y^(2))^k =4r^(2)x^(2)y^(2) , Then the value of k is

A plane meets the coordinate axes at A ,Ba n dC respectively such that the centroid of triangle A B C is (1,-2,3)dot Find the equation of the plane.

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