Conic Sections and polar coordinates

Hello

I'm stuck on this question Word for word from the text

"A.) decide whether the equation

$\displaystyle \[9x^2+6xy+y^2-12x-4y+4=0\]

$

represents a parabola an elipse or a hyberbola

b.) show that the graph of the equation in part A is the line $\displaystyle y=-3x+2$

my problem is that I cannot find the angle, in all the othe questions the angle worked out to be a special triangle but in this one I have tried applying $\displaystyle tan 2\alpha =\frac{B}{A-c}$ but I get an angle of 1/3

any help would be appreciated