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: 12,211 Thanks: 520 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.


Tags 
quadric, surfaces 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Cylinders And Quadric Surfaces  aaronmath  Calculus  0  February 12th, 2012 06:37 PM 
Quadric equation  Ockonal  Algebra  7  January 12th, 2012 04:35 AM 
Quadric surfaces and invariants  MagnusBL  Linear Algebra  0  December 1st, 2011 05:54 AM 
Quadratic surfaces  remeday86  Calculus  1  February 17th, 2009 04:40 AM 
Quadric equation  Ockonal  Calculus  3  December 31st, 1969 04:00 PM 