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Originally Posted by GW (Greg) Ross
Actually, that would have to be a half ellipse, since the two extremes are parallel. The sides of a parabola never reach parallel. 
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If you were to extend the length on the main cylindrical feature the extremes would be parallel, but if you to expand the height and width so that the poece would always be a perfect square the sides of the parabola would just be intersecting with the corners of the square shape and would continue in a parabolic "line"