A variable plane which is at a constant distance 3p from origin cuts the coordinate axes at A,B,C respectively. Show that locus of the centroid of the `triangleABC` is `1/x^2+1/y^2+1/z^2= 1/p^2`.

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 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

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 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 variable plane which is at a constant distance 3p from the origin O cuts the axes at L,M and N.Show that the locus of the points of intersection of the planes through L,M,N drwon parallel to the coordinate planes is 9(x^(-2)+y^(-2)+z^(-2))=p^(-2) .

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 locus of the centre of the sphere O A B Ci s a/x+b/y+c/z=2.

A plane meets the coordinates axes at L, M, N respectively, such that the centroid of the triangle LMN is (1,-2,3) . Find the equation of the plane.

A variable plane x/a+y/b+z/c=1 at a unit distance from origin cuts the coordinate axes at A, B and C. Centroid (x, y, z) satisfies the equation 1/x^2+1/y^2+1/z^2=K. The value of K is (A) 9 (B) 3 (C) 1/9 (D) 1/3

P is the variable point on the circle with center at C. C A and C B are perpendiculars from C on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle P A B is a circle with center at the centroid of triangle C A B and radius equal to the one-third of the radius of the given circle.

The coordinates of A and B are (1,3)and (2,1) respectively and P is a moving point on the straight line x+7y=12.Find the locus of the centroid of the triangle ABP.