Can we construct a parabola without plot infinite number of point?

Can we construct a parabola without plot infinite number of point? it is given that the only paper we have is a clean sheet of paper, not the graphing paper and we do not have a ruler, but we may have a striaghtedge

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If you have a piece of string and two straightedges, you can do this (scroll down to section 2). – David Mitra Mar 31 '12 at 17:17
Ruler and straightedge constructions are for geometric figures consisting of only (straight) line segments. It is fundamentally not possible to draw a curve with a straightedge, unless you allow using it as a compass (attach a pen to one end, anchor the other end with the ability to spin around the anchor) -- then you can draw circles and arcs of circles. I don't know if this is mathematics, physics or just common sense. Actually, I can see doing some math here, given straightedge, compass, string, other devices, arranged in various ways, what curves can you draw? – David Lewis Mar 31 '12 at 17:34
@DavidLewis - you could use pin, for the complete method, read David Mitra's comment – Victor Mar 31 '12 at 17:41