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 variable plane at a distance of 1 unit from the origin cuts the axes at A, B and C. If the centroid D(x, y, z) of triangleABC satisfies the relation (1)/(x^2)+(1)/(y^2)+(1)/(z^2)=K, then the value of K 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 the locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

The normals at three points P,Q,R of the parabola y^2=4ax meet in (h,k) The centroid of triangle PQR lies on

Find the centre and radius of the sphere 2x^2+2y^2+2z^2-2x+4y+2z+3=0 .

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 plane meets the coordinate axes in A ,B ,C such that eh centroid of triangle A B C is the point (p ,q ,r)dot Show that the equation of the plane is x/p+y/q+z/r=3.

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

One vertex of the equilateral triangle with centroid at the origin and one side as x+y -2 =0 is

A plane passing through (1,1,1) cuts positive direction of coordinates axes at A ,Ba n dC , then the volume of tetrahedron O A B C satisfies a. Vlt=9/2 b. Vgeq9/2 c. V=9/2 d. none of these

If the plane 2x + 3y + 4z=1 intersects X-axis, Y-axis and Z-axis at the points A, B and C respectively, then the centroid of a Delta ABC is …....