SOLUTION: For 3x² + xy + 3y² = 1, find Θ, the angle of rotation about the origin, to the nearest degree.

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Question 1034392: For 3x² + xy + 3y² = 1, find Θ, the angle of rotation about the origin, to the nearest degree.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The angle of rotation of axes theta that would eliminate the xy term from the conic Ax%5E2+%2BBxy+%2BCy%5E2+%2B+Dx+%2B+Ey+%2BF+=+0+is
cot%282%2Atheta%29+=+%28A+-+C%29%2FB.
==> cot%282%2Atheta%29+=+%28A+-+C%29%2FB+=+%283-3%29%2F1+=+0.
==> tan%282%2Atheta%29+=+infinity ==> 2%2Atheta+=+90%5Eo ==> highlight%28theta+=+45%5Eo%29.