introduction to three dimensional geometry

Let P(x,y,z)

Given PA +PB =10

i.e PA =  10 - PB

Squaring both sides ,

PA² =  (10 - PB)²  =100 + PB²  - 20PB

(x-4)²  +  y ²  +  z ²  = (x +4)²  + y² + z ²   -20[  ((x +4)²  + y² + z ^2 )

simplifying , we get

4x + 25=5 [  ((x +4)²  + y² + z ^2 )

Square both sides again and simplify