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I am required to calculate the rotation angle needed to come into standard form without x y product term (to make axes parallel to conic axes) in trying to find solution of problem:

A conic $M$, in standard or reflected standard form, is rotated through an angle $r$ about the origin to obtain the conic $N$ with equation $$ax^2+bxy+cy^2=d$$ where $a=2$, $b=2$, $c=34$ and $d=54$.

To two decimal places what is the absolute value of the angle $r$ in degrees? As usual, do not give any units in your answer. Do not include a minus sign in your answer.

This is the solution I came up with: $$2x^2+2xy+34y^2=54$$ $$A=2 \quad B=2 \quad C=34 \quad D=54$$

$A \neq C, $ \begin{align*} \therefore \theta &= \tfrac{1}{2} \tan^{-1} \tfrac{2}{2-34} \\ &= \tfrac{1}{2} (-0.06242) \\ &= -0.03121 \\ &\simeq -0.03 \end{align*} Someone please check my work. Thanks.

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    i don't understand what are you asking?2012-10-03
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    @Avatar i am asking if it is correct according to the question. Nice nick by the way.2012-10-03
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    you did it right and thanks for the compliment :)2012-10-03

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