A variable plane is at a distance $k$ from origin and meets the coordinate axes at the points $A,B,C$ respectively. then the locus of centroid of the $\Delta\:ABC$ is ?

Question

$(a)\:\large\frac{1}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\:\:\qquad\:(b)\:\large\frac{3}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\:\:\qquad\:(c)\:\large\frac{4}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}\:\:\qquad\:(d)\:\large\frac{9}{k^2}=\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$