SOLUTION: My question is how do I arrive at the books answer? Book says, “Determine the appropriate rotation formula to use so that the new equation contains no xy-term.” 25x^2-36xy+

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Question 1165103: My question is how do I arrive at the books answer?
Book says, “Determine the appropriate rotation formula to use so that the new equation contains no xy-term.”
25x^2-36xy+40y^2-12sqrt(13)x-8sqrt(13)y=0
Answers in the back of the book say x=sqrt(13)/13(3x’-2y’) and y=sqrt(13)/13(2x’+3y’)
The angle I get is cot(2theta)=5/13 so cos(2theta)=5/sqrt(194) which doesn’t lead to the books answer.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The angle of rotation θ is given by

cot%282theta%29=%28A-C%29%2FB+=+%2825-40%29%2F%28-36%29=%28-15%29%2F%28-36%29=5%2F12

You have 5/13, not 5/12.  Try it with that.  Everything should come out a lots
nicer.  If you still have trouble let me know in the space below and I'll
get back to you by email.

Also, remember, there are two angles that will eliminate the xy term. The
back of the book may use the other one from the one you use.

Edwin