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Math Help - help with level curve

  1. #1
    Member
    Joined
    Nov 2008
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    146

    help with level curve

    I have
    x^2 +xy

    I want to sketch level curves for it but I'm stuck at simplifying it. I can factor out the x or complete the square but how do I find out what the curve is?

    so another form is
    (x+Ży)^2 - 0.25y^2

    so if I let c = 2 for example I'll get

    (x+Ży)^2 - 0.25y^2 = 2

    what do I do now?
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  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
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    Detroit, MI
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    Re: help with level curve

    If f(x,y)=x^2+xy then to plot level curves we choose values of a constant c such that f(x,y)=c.

    If f=c, then c=x^2+xy\Rightarrow{y}=\frac{c-x^2}{x}. Now, graph y as a function of x in the plane for varying values of c
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