Axis rotation graphing

**Greymalkin** · September 2nd 2012, 11:40 PM

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.

**Greymalkin** · September 2nd 2012, 11:57 PM

Think I found the error in $y=\frac{x'+y'\sqrt3}{2}$

**blazeminds** · September 3rd 2012, 04:33 AM

yup right grey error found

Thread: Axis rotation graphing

LinkBack

Thread Tools

Display

Axis rotation graphing

Re: Axis rotation graphing

Re: Axis rotation graphing

Similar Math Help Forum Discussions

Volume of rotation (y-axis)

Volumes by Rotation about y-axis

volume by rotation about x axis

Verification on a x-axis rotation

Rotation around an axis

Search Tags