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Problem with level sets

  1. Feb 7, 2016 #1
    First of all sorry for my english skills.
    1. The problem statement, all variables and given/known data

    Im trying to get the set levels of this function:
    f(x,y)=(x-y)/(1+x^2+y^2)=z

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

    3. 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 im doing wrong.
    Thanks
     
  2. jcsd
  3. Feb 7, 2016 #2

    Samy_A

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    Never mind, I was mistaken, apologies.
     
  4. Feb 7, 2016 #3

    Samy_A

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    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.
     
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