Answer
$y=1$
Work Step by Step
We know that the distance from (0,0,0) to (x,y,z), equals the distance from (0,2,0) to (x,y,z):
Use the distance formula
$\sqrt{x^{2}+y^{2}+z^{2}}=\sqrt{x^{2}+(y-2)^{2}+z^{2}}\quad$
square both sides:
$ x^{2}+y^{2}+z^{2}=x^{2}+(y-2)^{2}+z^{2}\quad$
simplify:
$y^{2}=y^{2}-4y+4$
$4y=4$
$y=1$
This is the plane parallel to the xz plane, containing (0,1,0).
