I am a beginner in this area. So if i make wording related mistakes pls correct me.
Generator means line contained entirely in a surface. There is a problem in my textbook which goes like this --> "generator of hyperboloid of 1 sheet cuts principle elliptic section in 2 points". How can generator cuts in 2 points at principle elliptic section? Principle elliptic section means in hyperboloid, ellipse section at origin...
I am trying to visualise using this diagram... it cuts in only 1 point.. http://mathworld.wolfram.com/One-SheetedHyperboloid.html
It appears that this text uses the singular “generator” to mean the pair of lines through a point on a doubly-ruled surface. This grammatically singular-number word is consistently used in a plural context in the text snippet that you’ve provided. I expect that this will be the case if you go back to where it introduces the term “generator” and examine its definition.