Question

A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is `1/x^2 + 1/y^2 + 1/z^2 = 1/p^2`

Answer 1

Let the equation of the plane be

From (ii), we have

a = 3α ,b = 3β and c = 3γ

Substituting the values of a, b, c in (iii), we obtain