Final answer:
The equation x² + xy + y² = 27 represents an ellipse.
Step-by-step explanation:
The equation x² + xy + y² = 27 represents an ellipse. An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is constant. In this case, the two foci are each located at a distance of √27 units away from the center.