The Locus of a point for which the sum of the squares of the distances from the coordinate axes is 16 units is

Suppose that P(x,y,z) be any point on the locus. The perpendicular distance from P(x1,y1,z1) to the x− axis is y2+z2The perpendicular distance from P(x1,y1,z1) to the y− axis is x2+z2The perpendicular distance from P(x1,y1,z1) to the z− axis is x2+y2Hence, the sum of the squares of the distances from the point P(x1,y1,z1) to the coordinate axes is 2(x2+y2+z2)Therefore, the locus  a point for which the sum of the squares of the distances from the coordinate axes is 16 units is x2+y2+z2=8