Ruled surfaces help

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1. May 28, 2015

rulo1992

Hello, I am studying for an analytic geometry final but I am totally lost for this problem... We didn't even cover this topic in class (my prof didn't show up for class for two weeks) and I have no clue on how to do it. If anyone could help I would appreciate it.

Question: Prove that the equation: $$x^2-y^2+xy-1=0$$ is a ruled surface.

I understand that a ruled surface is a surface composed of straight lines but that is as far as my knowledge goes for this question... Again any help is appreciated.

2. May 28, 2015

SteamKing

Staff Emeritus
You're close, but this article gives a more complete definition of ruled surfaces:

http://en.wikipedia.org/wiki/Ruled_surface

3. May 28, 2015

Staff: Mentor

Unrelated to your question -- the homework template is required. If you post a question again, please don't delete the three parts.

4. May 28, 2015

LCKurtz

With the $z$ variable missing, isn't this a cylindrical surface? For any fixed $(x,y)$ satisfying the equation, what happens to $(x,y,z)$ as you vary $z$?