Hi,

Please help me with this problem. I tried to solve it but I got stuck ...

Problem: Rotate the axes so that the new equation contains no xy-term. Discuss the new equation.

x^2 + 2xy + y^2 - 8x + 8y = 0

Here is what I got so far:

Solution:

A = 1, B = 2, C =1

cot 2 theta = (A - C) / B ==> (1 - 1)/2 ==> 0/2

(cot^2 theta - 1)/ 2 cot theta = 0/2

2 cot^2 theta - 2 = 0

2(cot^2 theta - 1) = 0

2(cot theta - 1) (cot theta + 1) = 0

cot theta = 1

theta = 45 degree

x = x' cos theta - y' sin theta

x = x' cos 45 - y' sin 45

y = x' sin 45 + y' cos 45

i got to this far and plug in to the original equation and simplied it. But I don't know what to do after that. Please help me!

Thank you!