Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quadratic Forms

  1. Apr 7, 2006 #1
    Write the equation in terms of new caraibles so that it is in standard position and identify the curve

    [tex] 3x^2 - 4xy = 2 [/tex]

    here a = 3, b = -4, c = 0 , [tex] d = \sqrt{(-4)^2+(3-0)^2} = 5 [/itex]

    [tex] \cos\theta = \frac{a+c-d}{\sqrt{b^2 + (a+c-d)^2}} = \frac{-2}{2\sqrt{5}} [/tex]
    [tex] \sin\theta = \frac{b}{\sqrt{b^2 + (a+c-d)^2}} = \frac{4}{\sqrt{20}} [/tex]

    so [tex] P = \frac{1}{\sqrt{5}} \left(\begin{array}{cc} -1&-2 \\ 2&-1 \end{array}\right) [/tex]

    from X = PY i get
    [tex] x = \frac{-1}{\sqrt{5}} (x_{1}-2y_{1}) [/tex]
    [tex] y = \frac{-1}{\sqrt{5}} (2x_{1}+y_{1}) [/tex]
    where x1 and y1 are the new variables
    is this fine??

    is this how you get the change of variables??
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: Quadratic Forms
  1. Quadratic Form (Replies: 3)

  2. Quadratic forms (Replies: 3)

Loading...