A variable plane is at a distance

MATHEMATICS · Single correct · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry

Problem

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

\triangle ABC

is (1)

x^{-2} + y^{-2} + z^{-2} = k^{-2}

(2)

x^{-2} + y^{-2} + z^{-2} = 4k^{-2}

(3)

x^{-2} + y^{-2} + z^{-2} = 16k^{-2}

(4)

x^{-2} + y^{-2} + z^{-2} = 9k^{-2}