Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By MaxJasper

Math Help - Question on Quadric Surfaces

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    Texas
    Posts
    49

    Question on Quadric Surfaces

    Hey everyone,
    I am having a bit of difficulty understanding a problem. It says: The trace of the graph of z = f(x,y) = \ x^2 + 2y^2 on the plane z=3, is which of the following conic sections?

    At first glance, the equation of z = \ x^2 + y^2 is an elliptic paraboloid. However, if I plug-in z=3 into the equation, I get
    \ x^2 + 2y^2 = 3, which is an ellipse I believe. So, exactly how am I suppose to solve this problem. Am I already correct in assuming the answer is an ellipse? Or is my understanding of the problem incorrect.

    Any help and feedback is greatly appreciated, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: Question on Quadric Surfaces

    Here is intersection of plane z=3 with f(x,y):

    Attached Thumbnails Attached Thumbnails Question on Quadric Surfaces-elliptic-paraboloid.png  
    Thanks from Beevo
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2012
    From
    Texas
    Posts
    49

    Re: Question on Quadric Surfaces

    ^^^
    Thanks man. So basically, from the 3-d graph that you presented, it appears to be an elliptic paraboloid. But with the constant z that is given, it appears to be an ellipse in the xy plane ( I believe).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quadric surfaces problem please help.
    Posted in the Calculus Forum
    Replies: 8
    Last Post: September 21st 2009, 05:11 PM
  2. Sketching Quadric Surfaces
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 25th 2008, 10:27 AM
  3. help with quadric surfaces
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 3rd 2008, 12:15 AM
  4. Quadric Surfaces
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 8th 2008, 11:00 PM
  5. sketch quadric surfaces
    Posted in the Calculus Forum
    Replies: 6
    Last Post: January 6th 2007, 02:03 PM

Search Tags


/mathhelpforum @mathhelpforum