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 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(k^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 variable line through the point P(2,1) meets the axes at Aa n dB . Find the locus of the centroid of triangle O A B (where O is the origin).

If a plane meets the equations axes at A ,Ba n dC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.

If a plane meets the equations axes at A ,Ba n dC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.

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 straight line passes through (1,2) and has the equation y-2x-k =0 . Find k.

A plane passes through a fixed point (a ,b ,c)dot Show that the locus of the foot of the perpendicular to it from the origin is the sphere x^2+y^2+z^2-a x-b y-c z=0.

A rod of length k slides in a vertical plane, its ends touching the coordinate axes. Prove that the locus of the foot of the perpendicular from the origin to the rod is (x^2+y^2)^3=k^2x^2y^2dot

A variable line y=m x-1 cuts the lines x=2y and y=-2x at points Aa n dB . Prove that the locus of the centroid of triangle O A B(O being the origin) is a hyperbola passing through the origin.