A variable plane which remains at a constant distance from the origin cuts the…

MATHEMATICS · Subjective · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

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

x^2 y^2 + y^2 z^2 + z^2 x^2 = \frac{k}{p^2} x^2 y^2 z^2

, then

\sqrt[3]{2k}