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Sketching a level curve

  1. Mar 30, 2010 #1
    im having trouble with sketching a level curve

    ex. equation: f(x,y) = x^2 + 2y^2

    i cant run it .. (edit: sorry, -cant run it by matlab) .. :(

    cant solve cant graph cant all .... in short, cant any attempt at a solution :(((

    thank for your help ..
    Last edited: Mar 30, 2010
  2. jcsd
  3. Mar 30, 2010 #2


    Staff: Mentor

    What do you mean you can't "run it?"

    Level curves are two-dimensional slices of a surface in three dimensions. Pick several values for z and sketch graphs of the resulting curves.

    For example, if z = 0, what's the graph of the equation x^2 + 2y^2 = 0 look like?
    If z = 1, what's the graph of the equation x^2 + 2y^2 = 1 look like?
    If z = -1, what's the graph of the equation x^2 + 2y^2 = -1 look like?

    And so on...
  4. Mar 30, 2010 #3

    When I had to sketch level curves, my teacher showed me a nice and easy to understand method:
    Your equation is f(x,y) = x^2 + 2y^2 . Write it as z = x^2+2y^2
    which could also be re-written as z=(x^2/1)+(y^2/1/2)

    Now that you have a clearer idea of what this could represent : if z=k a constant then for a certain z you have an ellipse of k=(x^2/1)+(y^2/1/2)
    Sketch it for some values and then connect the elements together. Since z can't be negative (x and y are both squared) it will be something like a parabola going up in the z-dir. So I guess it is a paraboloid, where each "slice" taken in z=k plane is an ellipse given by k=(x^2/1)+(y^2/1/2).
  5. Mar 30, 2010 #4
    thank you for your attention :)
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