SOLUTION: For x² - 4xy - 2y² - 6 = 0, find Θ, the angle of rotation about the origin, to the nearest degree.

x² - 4xy - 2y² - 6 = 0

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 45° or 
if A = C

Your equation is

x² - 4xy - 2y² - 6 = 0

In this case A=1, B=-4, C=-2, D=0, E=0, F = -6

Substituting in





Choosing the smallest positive angle:
 or 
 or 

Edwin