Final answer:
The equation given is a rotated ellipse because it has x² and y² terms with the same coefficient and an xy term.
Step-by-step explanation:
The equation 2x²-4xy+y²+3=0 represents a conic section, and by analyzing the coefficients and terms, we can classify the type of conic it represents. When a conic section equation has both x² and y² terms and the coefficients of these squared terms are the same but with opposite signs, we typically expect a hyperbola. However, because the coefficients are both positive and the same (2x² and y² when factoring out the -4xy), this suggests that we are dealing with either a circle or an ellipse, but the presence of the xy term indicates that this is a rotated conic. Without the xy term, it would be an ellipse. Given the equation does not conform exactly to the standard forms of conic sections, we can consider it to be a rotated ellipse, as a circle would not have a cross term in x and y.