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Originally Posted by Richard
GW is right. The curved edge is elliptical, not parabolic. Referring again to the the mathworld site, an ellipse is a section through a cylinder (a circle is the special case in which the section plane is perpendicular to the cylinder's axis), while a parabola is a conic section (section through a cone).
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Correct. Specifically, a parabola is the special case where the section plane is parallel to one "edge" of the cone, so that the curve never closes on itself:
http://mathworld.wolfram.com/ConicSection.html