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Level curves (or contour curves) of a certain 3 dimensional function.

  1. Feb 5, 2014 #1
    I can't seem to quite comprehend the level curves for f(x,y)=xy. I realize this should be very simple yet the answer eludes me. f(x,y) for this the two dimensional representation of this function will be substituted with k(a fixed number). I would greatly appreciate somebody explaining my contour diagram to me and what the graph of k(fixed number)=xy even resembles in two dimensions and why.
     
  2. jcsd
  3. Feb 5, 2014 #2

    ShayanJ

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    Gold Member

    [itex] xy=k \Rightarrow y=\frac{k}{x} [/itex]
    [itex] k=0 \Rightarrow \left\{ \begin{array}{cc} y=0 \ \ \ x \ axis \\ x=0 \ \ \ y \ axis \end{array} \right. [/itex]
    [itex] k\neq 0 \Rightarrow [/itex] hyperbolas with x and y axes as asymptotes.
     
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