generatrix
Quick Summary
In geometry, a generatrix is a point, line, or surface that generates a line, surface, or solid through its motion.1
A common example is a cone, which is a surface traced by a moving straight line (the generatrix) that always passes through a fixed point called the vertex. This motion is guided by a closed plane curve known as the directrix. The generatrix of a cone is considered to be infinitely long, extending in both directions from the vertex, creating two infinite parts called nappes.2
A directrix can also be a fixed curve that a generatrix relates to in generating a geometric figure. Specifically, it can be a straight line where the distance from any point on a conic section to this line is in a fixed ratio to the distance from that point to a focus.3
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