A variable plane is at a distance, k from the origin and meets the coordinates axis in A, B , C. Then, the locus of the centroid of `triangleABC` is

Options

A. `(1)/(x^(2)) +(1)/(y^(2))+ (1)/(z^(2)) = (1)/(p^(2))`
B. `(1)/(x ^(2))+ (1)/(y ^(2)) + (1)/(z ^(2)) = (9)/(p^(2))`
C. `(1)/(x^(2)) + (1)/(y ^(2)) + (1)/(z ^(2))= (2)/(p^(2))`
D. `(1)/(x ^(2)) + (1)/(y ^(2)) + (1)/(y ^(2)) = (4)/(p ^(2))`

Answer

B