Question 1036875
<pre><b>
x² - 4xy - 2y² - 6 = 0

The angle of rotation {{{theta}}} 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 {{{tan(2theta)=B/(A-C)}}} or 45° or {{{pi/4}}}
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

{{{tan(2theta)=B/(A-C)}}}
{{{tan(2theta)=(-4)/(1-(-2))}}}
{{{tan(2theta)=(-4)/(1+2)}}}
{{{tan(2theta)=-4/3}}}
Choosing the smallest positive angle:
{{{2theta=2.214297436}}} or {{{2theta="126.8698976°"}}}
{{{theta=1.107148718}}} or {{{theta="63.43494882°"}}}

Edwin</pre></b>