Help with Proving Ruled Surface Equation

[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.

 

[SteamKing]

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.

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

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

 

[Mark44]

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.

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

 

[LCKurtz]

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.

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 $z$?