Question

Find the locus of a point, the sum of the squares of whose distances from the planes x + y + z = 0, x – z = 0, x – 2y + z = 0 is 9.

Answer 1

Let the point be

It is given that, 

= 7x² + 10y² + 7z² + 2xz – 4xy – 4yz = 9.