My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 12th, 2012, 07:40 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
aaron-math is offline  
 
February 12th, 2012, 07:44 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.
Fantini is offline  
February 12th, 2012, 07:53 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:





aaron-math is offline  
February 12th, 2012, 08:15 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.
Fantini is offline  
February 12th, 2012, 08:15 PM   #5
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,206
Thanks: 513

Math Focus: Calculus/ODEs
Re: Quadric Surfaces

We are given:



Completing the square as advised:





We then have a one-sheeted hyperboloid.
MarkFL is offline  
February 12th, 2012, 08:19 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.
aaron-math is offline  
February 12th, 2012, 08:19 PM   #7
Newbie
 
Joined: Aug 2010

Posts: 22
Thanks: 0

Re: Quadric Surfaces

Oops, got a sign wrong there. Thanks Mark, fixed.
Fantini is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
quadric, surfaces



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Cylinders And Quadric Surfaces aaron-math Calculus 0 February 12th, 2012 07:37 PM
Quadric equation Ockonal Algebra 7 January 12th, 2012 05:35 AM
Quadric surfaces and invariants MagnusBL Linear Algebra 0 December 1st, 2011 06:54 AM
Quadratic surfaces remeday86 Calculus 1 February 17th, 2009 05:40 AM
Quadric equation Ockonal Calculus 3 December 31st, 1969 04:00 PM





Copyright © 2018 My Math Forum. All rights reserved.