February 14th, 2010, 09:53 AM  #1 
Member Joined: Sep 2007 Posts: 49 Thanks: 0  Surface
Describe th surface: x^2y^2=1 So if it's in 2D, it's must be hyperbolas. However, if I put it in 3D, I'm unsure because according to what's written on my book, it says If one of the variables x,y or z is missing from the equation of a surface, then the surface is a cylinder. Though I was considering other options like Hyperbolic Paraboloid, but the only problem is the general formula is z/c=x^2/a^2  y^2/b^2, and there is a z here. In that case, usually we can set z to 0, and so on. But in my original equation, z is never there, so that's the part I'm confused about. Thanks for help. 
February 14th, 2010, 12:32 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,104 Thanks: 1907 
Believe the book.

February 14th, 2010, 02:09 PM  #3 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Surface
It's a cylinder  but not the ordinary kind. It's a hyperbolic cylinder. If you imagine the xy plane as the page of a book, and the z axis as pointing out of the page, then you can envision drawing the graph of x²y² = 1 on the page, and then building a cardboard wall upwards from the graph. 
February 15th, 2010, 07:54 PM  #4 
Member Joined: Sep 2007 Posts: 49 Thanks: 0  Re: Surface
Thanks, aswoods. It helps a lot!!


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