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I figured out that θ is 30 degrees. After simplifying I still could not eliminate the xy-term: I ended up with:"Rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. (Use xp for x and yp for y' in your answer. Rotate the coordinate axes through an angle θ with 0 ≤ θ ≤ π/2.)"

13x^{2}+ 6√3xy + 7y^{2}– 32 = 0

10x

^{2}- 6xy + 10y

^{2}+ 3(sqrt(3))x

^{2}- 3(sqrt(3))y

^{2}-32 = 0

note: the x and y terms above are in prime form (I just don't know how to show that on a forum)

As you can see I still have a negative 6xy. Considering the previous HW questions I've solved eliminated the xy terms easily, I'm at a loss with what to do should I encounter leftover xy terms.

Thanks in advance.

EDIT: You know this always happens to me, whenever I just ask a question/post one, I've solved it. I'm sorry, but I've figured it out now. (Calculating an earlier step incorrectly).

However, a question still stands. Provided the equation doesn't solve out neatly and has left over xy terms, is there a way around it?