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Conic sections may be defined in terms of the "focus-directrix property", as the loci of points that satisfy a particular relationship involving a point called the focus and a line called the directrix. While the name "focus" for the point seems easily explicable, the name "directrix" for the line is less so (to me). Where did it originally come from? Is the "-trix" suffix supposed to indicate that it is feminine in some way?

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  • $\begingroup$ This could help with your question mathworld.wolfram.com/ConicSectionDirectrix.html $\endgroup$ – user242559 Mar 5 '17 at 22:12
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    $\begingroup$ The word directrix names in latin a feminine thing (line is feminine noun in latin) that directs. The -trix works like that, and is the femine version of -tor: it indicates a feminine agent: dominatrix, or executrix, aviatrix, generatrix, and so on. $\endgroup$ – Mariano Suárez-Álvarez Mar 5 '17 at 22:20
  • $\begingroup$ So you are saying that because "line" is a feminine noun, "director" is modified to take a feminine form, leading to "directrix"? That seems feasible, but the word for "line" isn't anywhere to be seen; only the word "director/-trix". Or am I showing my ignorance of how grammatical gender works in Latin? $\endgroup$ – Hammerite Mar 5 '17 at 22:29
  • $\begingroup$ It is not «feasible»: it is just like that — I am not making a guess: I am telling you how it is. The line is the directrix: if it were a point it would be the director. It is not an adjective, but a noun. It is the line that directs the conic. $\endgroup$ – Mariano Suárez-Álvarez Mar 5 '17 at 22:31
  • $\begingroup$ By the way, does director circle have masculine nature? $\endgroup$ – Ng Chung Tak Mar 5 '17 at 22:40
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I guess the name comes from the fact that the directrix is a fixed line, thus specifying a fixed direction.

According to merriam-webster's etymology: directrix is the "feminine of Late Latin director".

I think directrix is a late Latin translation of the ancient greek work "διευθετούσα" -used by Pappus of Alexandria who lived during the hellenistic period- which is a feminine participle meaning smt like "the one settling the thing". Maybe this discussion on PhysicsForums might be of interest in tracing the origins of the term directrix.

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A not-entirely-useful entry from the "Earliest Known Uses of Some of the Words of Mathematics" pages:

According to the DSB, Jan de Witt (1625-1672) "is credited with introducing the term 'directrix' for the parabola, but it is clear from his derivation that he does not use the term for the fixed line of our focus-directrix definition."

DSB = The Dictionary of Scientific Biography. C. C. Gillispie (editor in chief) New York : Charles Scribner’s Sons, 1970-1980.

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