If a circle of constant radius 3K passes through the origin and meets the axes at A&B.the locus of the centroid of `triangleOAB` is

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

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

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 variable plane which is at a constant distance 3p from the origin O cuts the axes at A,B,C. Show that the locus of the centroid of the triangle ABC is x^(-2)+y^(-2)+z^(-2)=p^(-2) .

A variable line is at constant distance p from the origin and meets the co-ordinate axes in A, B. Show that the locus of the centroid of the triangleOAB is x^(-2)+y^(-2)=9p^(-2)

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 variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C. Show that the locus of the centroid of the tetrahedron OABC is (1)/(x^2)+(1)/(y^2)+(1)/(z^2)=(16)/(p^2) .

A circle of constant radius 'r' passes through origin O and cuts the axes of coordinates in points P and Q, then the equation of the locus of the foot of perpendicular from O to PQ is

A variable plane is at a constant distance p from the origin and meets the coordinate axes in A,B and C , show that the locus of the centroid of the tetrahedron OABC os 1/x^2+1/y^2+1/z^2= 16/p^2

From a point on the circle x^2+y^2=a^2 , two tangents are drawn to the circle x^2+y^2=b^2(a > b) . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.