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

Options

A. Locus of centroid of tetrahedron OABC is `x ^(2) y ^(2) +y ^(2) z^(2) + z ^(2) x ^(2) = (16)/(p ^(2)) x ^(2) y ^(2) z ^(2)`
B. Locus of centroid of tetrahedron OABC is `x ^(2) y ^(2) + y ^(2) z ^(2) + z ^(2) x ^(2) = (4)/(p ^(2))x ^(2)y^(2) z^(2)`
C. Parametric equation of the centroid of the tetrahedron is of the form `((p)/(4)sec alpha sec beta, (p)/(4) sec alpha cosec beta, (p)/(4) cos ec alpha ),alpha, beta in 0, 2pi)-pi//2,pi,3pi //2)`
D. None of the above

Answer

A, C