Consider a point on curve P and its (nearest) image on curve P'. The midpoint between those points is on the line of reflection. That line is the x-axis.
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<em>Additional comment</em>
The curve is symmetrical about the y-axis, so each point on P also has an image point that is its reflection across the origin. The reflection of P could be across both the x- and y-axes, or (equivalently) across the origin. We don't know the meaning of "xy-axis", so we suspect that is a red herring. The best choice here is "x-axis."
