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Thread: help with level curve

  1. #1
    Member
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    Nov 2008
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    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 $\displaystyle f(x,y)=x^2+xy$ then to plot level curves we choose values of a constant $\displaystyle c$ such that $\displaystyle f(x,y)=c$.

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