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Help finding an equation for the level curve

  1. Oct 3, 2005 #1
    Hey guys, I tried it out, but I just don't get it. I have to find the equation for the level curve f(x, y)=(x^2 + y^2)e^(xy); that contains the point P(1,0). By the way, e^(xy) is read e to the x times y, just in case.


    What I did, which looks wrong the whole way was:

    (x^2 + y^2)e^(xy) ---> (x^2)(e^(xy)) + (y^2)(e^(xy)) = 0

    ---> ln(x^2) + ln(e^(xy)) = (-1) ln(y^2) + ln(e^(xy))
    ---> 2ln(x) + xy = (-1) (2ln(y) + xy)
    ---> 2ln(x) = (-1)(2ln(y))


    ...and i'm stuck there. Could anyone help correct this, or if possible, help continue? Thanks a bunch.
     
  2. jcsd
  3. Oct 4, 2005 #2

    CarlB

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    Science Advisor
    Homework Helper

    I thought that the equation you need to solve would be written as:

    [tex]f(x,y) = f(1,0)[/tex]

    Or

    [tex](x^2+y^2)e^{xy} = e[/tex]

    From here, my instinct would be to convert to polar coordinates.

    Carl
     
  4. Oct 4, 2005 #3

    ehild

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    Homework Helper
    Gold Member

    Why did you write that

    [tex]f(x,y)=(x^2+y^2)e^{xy}=0[/tex]?

    You want a level curve. That means that f(x,y) is the same for all points of the curve.The level curve should contain the point with x=1, y=0. Plug in these values and see what you get for f(x,y).

    ehild
     
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