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Quadratic Forms 
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#1
Apr706, 04:31 PM

P: 1,439

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+(30)^2} = 5 [/itex] [tex] \cos\theta = \frac{a+cd}{\sqrt{b^2 + (a+cd)^2}} = \frac{2}{2\sqrt{5}} [/tex] [tex] \sin\theta = \frac{b}{\sqrt{b^2 + (a+cd)^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?? 


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