Question

A point P moves on a plane x/a + y/b + z/c = 1. A plane through P and perpendicular to OP meets the co-ordinate axes at A, B and C. If the plane through A, B and C and parallel to the planes x = 0, y = 0, z = 0 intersect at Q, find the locus of Q.

Answer 1

Given plane is x/a + y/b + z/c = 1 ....(i)

Let P

The equation of the normal through P and normal to OP is

From Eq. (iv), we get