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February 14th, 2010, 09:53 AM   #1
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Describe th surface: x^2-y^2=1
So if it's in 2-D, it's must be hyperbolas. However, if I put it in 3-D, 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.
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February 14th, 2010, 12:32 PM   #2
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Believe the book.
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February 14th, 2010, 02:09 PM   #3
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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 x-y = 1 on the page, and then building a cardboard wall upwards from the graph.
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February 15th, 2010, 07:54 PM   #4
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Re: Surface

Thanks, aswoods. It helps a lot!!
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