Register to reply 
Quadratic Forms 
Share this thread: 
#1
Apr706, 04:31 PM

P: 1,440

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?? 


Register to reply 
Related Discussions  
Matrix forms of quadratic equations  Precalculus Mathematics Homework  4  
Quadratic forms  Calculus & Beyond Homework  3  
Quadratic forms of symmetric matrices  Linear & Abstract Algebra  6  
Binary quadratic forms  Linear & Abstract Algebra  11  
Quadratic forms, linear algebra  Introductory Physics Homework  3 