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Math Help - Axis rotation graphing

  1. #1
    Junior Member Greymalkin's Avatar
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    Axis rotation graphing

    Graph x^2-2\sqrt{3}xy+3y^2-12\sqrt{3}x-12y

    I seem to be getting lost in the tedious amount of algebra involved, please find my mistakes:

    \text{Angle=}cot2\theta=\frac{1}{\sqrt{3}}=\frac{6  0^\circ}{2}=30^\circ
    x=x'cos30^\circ-y'sin30^\circ=\frac{x'\sqrt3-y'}{2}
    y=x'sin30^\circ+y'cos30^\circ=\frac{x'\sqrt3+y'}{2  }

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

    x^2-2\sqrt{3}xy+3y^2-12\sqrt{3}x-12y



    (\frac{x'\sqrt3-y'}{2})^2-2\sqrt3(\frac{x'\sqrt3-y'}{2})(\frac{x'\sqrt3+y'}{2})+3(\frac{x'\sqrt3+y'  }{2})^2-12\sqrt3(\frac{x'\sqrt3-y'}{2})-12(\frac{x'\sqrt3+y'}{2})

    ~~~~~~~~~~~~~~~~~~~~~~

    (\frac{3(x')^2-2\sqrt3x'y'+(y')^2)}{4}-2\sqrt3(\frac{3(x')^2-(y')^2}{4}+3(\frac{3(x')^2+2\sqrt3x'y'+(y')^2}{4}-12\sqrt3(\frac{x'\sqrt3-y'}{2})-12(\frac{\sqrt3x'+y'}{2})=0

    The y^2 term ends up giving me another x'y' term that I find to be irreducible, which is nonsense because the equation is a fairly simple parabola.
    I would continue but I am certain the problem stems from this area or earlier.
    Last edited by Greymalkin; September 2nd 2012 at 11:48 PM.
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  2. #2
    Junior Member Greymalkin's Avatar
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    Re: Axis rotation graphing

    Think I found the error in y=\frac{x'+y'\sqrt3}{2}
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  3. #3
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    karachi
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    Re: Axis rotation graphing

    yup right grey error found
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