SOLUTION: Find to the nearest degree, the acute angle of rotation 1 that eliminates the xy term of -3x^2 + 3xy + 5y^2 - x + 2y - 6 = 0

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Question 860396: Find to the nearest degree, the acute angle of rotation 1 that eliminates the xy term of -3x^2 + 3xy + 5y^2 - x + 2y - 6 = 0
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find to the nearest degree, the acute angle of rotation 1 that eliminates the xy term of -3x^2 + 3xy + 5y^2 - x + 2y - 6 = 0
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Form:: Ax^2 +Bxy + Cy^2 + Dx + Ey + F = 0
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Angle of rotation:: cot(2t) = (A-C)/B = (-3-5)/3 = -8/3
2t = arc(tan(-3/8)) = -20.56 = 339.44
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Ans: t = 169.72
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Cheers,
Stan H.
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!
The other tutor gave you an obtuse angle, not an acute angle.

The angle of rotation  of the graph 

Ax² + Bxy + Cy² + Dx + Ey + F = 0

necessary to transform it into an equation in x' and y' which contains
no term in x'y'

is calculated by  or  if A = C

Your equation is

-3x² + 3xy + 5y² - x + 2y - 6 = 0

In this case A=-3, B=3, C=5, D=-1, E=2, F = -6









Find the reference angle for ,
using the inverse tangent function of a
calculator using . That gives
reference angle for  as 20.55604522

So the smallest positive value for 
that has tangent  is in QII, and is
180-20.55604522 = 159.4439548

So



and



To nearest degree, 80°

Edwin
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