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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? – Aang Oct 3 '12 at 7:50
@Avatar i am asking if it is correct according to the question. Nice nick by the way. – JackyBoi Oct 3 '12 at 7:54
you did it right and thanks for the compliment :) – Aang Oct 3 '12 at 8:08

Two problems:

1) The answer you gave is in radians, but the problem statement says it must be in degrees. So convert your unrounded answer to degrees, then round to two decimal places.

2) Your answer is negative, but the problem statement says not to include a minus sign in your answer. I'm not sure if you should write the absolute value of your answer, or add $180^\circ$ to the answer. The wording of the problem inclines me to the former: just remove the minus sign.

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