Answer
parabola and $\dfrac{-4}{3}$
Work Step by Step
Given: $9x^2-6xy+y^2+6x-2y=0$
This gives:
$A=9; B=-6, C=1$
Thus, $B^2-4AC=(-6)^2-4(9)(1)=36-36= 0$
This represents the equation of a parabola.
Now, $\cot 2 \phi=\dfrac{A-C}{B}=\dfrac{9-1}{-6}=\dfrac{-4}{3}$
