February 12th, 2012, 06:40 PM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Quadric Surfaces
Reduce the equation to one of the standard forms. Classify the surface. hyperbolic cylinder parabolic cylinder ellipsoid hyperbolic paraboloid cone elliptic cylinder elliptic paraboloid hyperboloid 
February 12th, 2012, 06:44 PM  #2 
Newbie Joined: Aug 2010 Posts: 22 Thanks: 0  Re: Quadric Surfaces
Aaron, have you tried completing the squares for x, y and z respectively? The answer should follow.

February 12th, 2012, 06:53 PM  #3 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: Quadric Surfaces
I get stuck when I get to the term because normally when you complete the square if the leading coefficient is not one, you divide through by that number to make it one. Here I can not divide through by (1) because it will make the other two squared terms have an coefficient of (1) I rewrite it as: 
February 12th, 2012, 07:15 PM  #4 
Newbie Joined: Aug 2010 Posts: 22 Thanks: 0  Re: Quadric Surfaces
Let's try: Defining we have . We have a hyperboloid of one sheet. 
February 12th, 2012, 07:15 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  Re: Quadric Surfaces
We are given: Completing the square as advised: We then have a onesheeted hyperboloid. 
February 12th, 2012, 07:19 PM  #6 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Re: Quadric Surfaces
Cool, thx guys, I will do it like that next time.

February 12th, 2012, 07:19 PM  #7 
Newbie Joined: Aug 2010 Posts: 22 Thanks: 0  Re: Quadric Surfaces
Oops, got a sign wrong there. Thanks Mark, fixed.


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