Answer
Ellipse
Work Step by Step
expand equation:
$2x^{2}-2xy=3y-y^{2}-2xy$
Simplify to one side:
$2x^{2}+y^{2}-3y=0$
Analyze:
$x^{2}$ and $y^{2}$ are both added with the same sign but $x^{2}$ is multiplied by a factor of 2 therefore it must be an ellipse
