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Math Help - A special type of function...

  1. #1
    anak
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    A special type of function...

    x^4 - (5x^2)(y^2) + 4y^4 = 0

    What do you call this type of function and how do you graph it? I can't seem to find any way on my '84
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  2. #2
    Super Member

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    Hello, anak!

    x^4 - 5x^2y^2 + 4y^4 \:= \:0

    What do you call this type of function and how do you graph it?

    I'm not familiar with any name for this type.
    It is a quartic function, but it is "degenerate".

    It factors: . (x^2 - y^2)(x^2 - 4y^2) \:=\:0

    Hence, we have: . \begin{array}{cc}x^2-y^2\:=\:0 \;\; \Rightarrow\;\; y^2 = x^2\;\;\Rightarrow\;\; y = \pm x  \\ x^2-4y^2\:=\:0 \;\;\Rightarrow\;\; y^2 = \frac{x^2}{4} \;\;\Rightarrow\;\; y = \pm\frac{1}{2}x\end{array}

    The graph is two pairs of lines intersecting at the origin.

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