Why am I getting complex radii for level sets of this function?

[parkerfisss]

First of all sorry for my english skills.
1. Homework Statement
Im trying to get the set levels of this function:
f(x,y)=(x-y)/(1+x^2+y^2)=z

Homework Equations

circle-> (x-xo)^2+(y-yo)^2=r^2

The Attempt at a Solution

(Leaving this here just to give a graph https://www.wolframalpha.com/input/?i=z=(x-y)/(1+x^2+y^2))
For z=0 its obvious a line y=x.

by taking z=1(or any z=/0 it should give us according to the graph circles of different radious):
x-y=1+x^2+y^2
#sum 2(1/2)^2 on both sides
x^2-x+(1/2)^2 +y^2+y+(1/2)^2= -1+2(1/2)^2
(x-1/2)^2+(y+1/2)^2=-1/2

This last equation means its a circle of radious sqrt(-1/2) with center in (1/2,-1/2).

So my question its why i get complex radious, and what I am doing wrong.
Thanks

 

[Samy_A]

Never mind, I was mistaken, apologies.

 

[Samy_A]

First of all sorry for my english skills.
1. Homework Statement
Im trying to get the set levels of this function:
f(x,y)=(x-y)/(1+x^2+y^2)=z

Homework Equations

circle-> (x-xo)^2+(y-yo)^2=r^2

The Attempt at a Solution

(Leaving this here just to give a graph https://www.wolframalpha.com/input/?i=z=(x-y)/(1+x^2+y^2))
For z=0 its obvious a line y=x.

by taking z=1(or any z=/0 it should give us according to the graph circles of different radious):
x-y=1+x^2+y^2
#sum 2(1/2)^2 on both sides
x^2-x+(1/2)^2 +y^2+y+(1/2)^2= -1+2(1/2)^2
(x-1/2)^2+(y+1/2)^2=-1/2

This last equation means its a circle of radious sqrt(-1/2) with center in (1/2,-1/2).

So my question its why i get complex radious, and what I am doing wrong.
Thanks

Actually my hint was correct, sorry for my own confusion.
Try your calculation for a non zero z (don't pick a specific value), and see for which z you get a real radius.