A Conic Has Equation $6 x ^ { 2 } + 3 y ^ { 2 } + x - 3 y = 1 - 3 \sqrt { 3 } x y$

Essay

A conic has equation $6 x ^ { 2 } + 3 y ^ { 2 } + x - 3 y = 1 - 3 \sqrt { 3 } x y$ .
(a) Use the discriminant to identify the conic.
(a) by graphing the conic with a graphing calculator.
(b) Confirm your answer in part
(c) Find the angle necessary to eliminate the $x y$ - term.