A variable plane cuts the and -axes at the points

MATHEMATICS · Subjective · CBSE · Mathematics · Three-Dimensional Geometry · IB Diploma Programme

Problem

A variable plane cuts the

x, y

and

z

-axes at the points,

A, B

and

C

, respectively such that the volume of the tetrahedron

OABC

remain constant equal to 32 cu units and

O

is the origin of the coordinate system.

Column I	Column II
(A) The locus of the centroid of the tetrahedron is	(p) $xyz = 24$
(B) The locus of the point equidistant from $O, A, B$ and $C$ is	(q) $(x^2 + y^2 + z^2) = 192 xyz$
(C) The locus of the foot of perpendicular from origin to the plane is	(r) $xyz = 3$
(D) If $PA, PB$ and $PC$ are mutually perpendicular, then the locus of $P$ is	(s) $(x^2 + y^2 + z^2)^3 = 1536 xyz$