Three Dimensional Geometry Part 2

Let P=(α,β,γ)
Distance of point P from the plane x+y+z=0 is
=‌

α+β+γ

√3

Distance of point P from the plane lx−nz=0 is
=‌

lα−nγ

√12+n2

and distance of point P from the plane x−2y+z=0 is
=‌

α−2β+γ

√6

According to the question,
∴ Locus is Comparing it with the given equation of locus, we get
2ln=I2+n2
⇒‌‌(I−n)2=0
⇒‌‌I−n=0