: any of the quill feathers of a bird's tail that are important in controlling flight direction
Merriam-Webster's little etymology blurb tells us the word RECTRIX is English, it is more commonly known in its Latin plural form (RECTRICES), and, by the way, it may also refer to a woman who rules or governs. Over. So...what do the feathers on a bird's ass have to do with a woman who rules or governs? Nothing. It just means that the word RECTRIX is also the feminine form for RECTOR, a man who rules or governs (as in, a university). I can't imagine the female head of university wanting to be called a RECTRIX. In Scotland the university RECTOR is technically the Lord RECTOR. I guess that would may his female counterpart the Lady RECTRIX.
An internet search for "lady RECTRIX" turns up nothing.
The above photo is the "tail end" of a Lord RECTOR of Glasgow University.