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Need help in drawing a level curve.

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    i want to draw a level curve for the following but im having some trouble.

    x-y^2/x^2+y


    2. Relevant equations



    3. The attempt at a solution

    I know i'm supposed to set c = x-y^2/x^2+y, but i can't find a way to set y in terms of x and c.
     
  2. jcsd
  3. Oct 10, 2011 #2

    Mark44

    Staff: Mentor

    Let me see if I have this straight. Your function is f(x, y) = x - (y2/x2) + y, right? That's what you wrote.
     
  4. Oct 10, 2011 #3
    Whoops, guess I should've added brackets.

    [x-y^2]/[x^2+y]

    sorry bout that.
     
  5. Oct 10, 2011 #4

    Mark44

    Staff: Mentor

    Much better.

    Your equation is z = (x - y2)/(x2 + y)

    The level curves are curves in some plane, z = c.

    For example, in the plane z = 1, the level curve is the equation (x - y2)/(x2 + y) = 1. Keep in mind that y can't equal -x2.

    Multiply both sides by x2 + y. What equation do you get?
     
  6. Oct 10, 2011 #5
    c(x^2+y) = (x-y^2)?
     
  7. Oct 11, 2011 #6

    Mark44

    Staff: Mentor

    So if you move all of the terms to one side, what do you get?
     
  8. Oct 11, 2011 #7
    cx^2 + cy - x + y^2 = 0

    so when c = 0 i get a parabola, but what about when c = 2 for example..?
     
    Last edited: Oct 11, 2011
  9. Oct 11, 2011 #8

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Complete the squares.

    2x2 - x + y2 +2y = 0

    2(x2 - (1/2)x) + y2 +2y = 0

    2(x2 - 2 (1/4)x + (1/4)2 -1/16 ) + y2 +2y + 1 - 1 = 0

    2(x - 1/4)2 + (y - 1)2 = 1 + 1/8

    (x - 1/4)2/(9/16) + (y - 1)2/(9/8) = 1

    Do similar for c in general.
     
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