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.)"
13x2 + 6√3xy + 7y2 – 32 = 0
10x2 - 6xy + 10y2 + 3(sqrt(3))x2 - 3(sqrt(3))y2 -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?