A variable plane which is at a constant distance 3p from the origin meets the axes in points A, B and C respectively. Show that the locus of the centroid of `Delta`ABC is `1/x^2+1/y^2+1/z^2=1/(p^2)`

A variable plane which is at a constant distance 6 p from the origin meets the axes in points A, B and C respectively. Show that the locus of the centroid of Delta ABC is 1/x^2+1/y^2+1/z^2=1/(4p^2)

A variable plane which is at a constant 6 p from the origin meets the axes in A,B and C respectively. Show that the locus of the centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(4p^(2))

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate 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 which remains at a constant distance 3p from the origin cuts the coordinate axes at A,B,C. Show that locus of the O centroid of the triangle ABC is (1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(p^(2)) .

A variable plane is at a constant distance 4p from the origin and cuts axes in A, B, C respectively. Show that the centroid of the tetrahedron OABC lies on : 1/x^2+1/y^2+1/z^2=1/p^2

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

A variable plane is at a distance k from the origin and meets the coordinates axes is A,B,C. Then the locus of the centroid of DeltaABC is

A variable plane which remains at a constant distance p from the origin cuts the co-ordinate axes at A, B, C. Through A,B,C planes are drawn parallel to the co-ordinate planes. Show that locus of the point of intersection is : x^(-2)+y^(-2)+z^(-2)=p^-2

The tangent PT and the normal PN to the parabola y^2=4ax at a point P on it meet its axis at points T and N respectively. The locus of the centroid of the triangle PTN is a parabola whose :