The determination of the major axis of an ellipse is based on the coefficients of the squared terms in its standard equation. If the "x^2" term has the larger denominator, the major axis is horizontal along the x-axis. Conversely, if the "y^2" term has the larger denominator, the major axis is vertical along the y-axis. The discussion clarifies that an ellipse cannot have a scenario where it lacks a defined major axis.
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