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Math Help - Oblique Conics?

  1. #1
    Junior Member masoug's Avatar
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    Oblique Conics?

    Hi,
    Is it possible to write the equation of an oblique conic in the y= form?
    For example, the equation 2x^2-4y^2+5xy=1 looks like Oblique Conics?-hyper.gif
    How do I find the y= version of it?

    Thanks!

    -Masoug
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  2. #2
    MHF Contributor
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    Not sure what you mean; looks like:
    4y^2 - 5xy - 2x^2 + 1 = 0
    Solve for y ?
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  3. #3
    Junior Member masoug's Avatar
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    Yes, how would I solve for y?
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  4. #4
    Super Member Quacky's Avatar
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    Treat the ' x' as a constant, and then substitute into the quadratic formula, or complete the square.

    4y^2 - 5xy - 2x^2 + 1 = 0
    Compare this with the general form of a quadratic:

    If ay^2+by+c=0

    then y=\displaystyle\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    Here, your a=4, b=-5x and c=-2x^2+1, so do the substitution.
    Last edited by Quacky; March 3rd 2011 at 11:01 AM.
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