# Calculate the angle of a rotated conic?

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

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.