Results 1 to 5 of 5

Math Help - intersection between two surfaces

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    8

    intersection between two surfaces

    I have two surfaces: x^2+y^2-z^2=0 (cone) and x^2-y^2-z=0 (hyperbolic paraboloid). I'm asked to find their intersection line in its parametric representation and to give the bounds of t.

    I tried to take z=x^2-y^2 from the second equation and to use it in the first one, but it leads to a complicated equation and I'm not sure that this is the correct way to deal with this question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Hint :

    Write for the cone:

    x=\left |{z}\right |\cos \theta,\;y=\left |{z}\right |\sin \theta\quad (\theta\in{[0,2\pi]})

    Substituting values into the paraboloid equation:

    z(z\cos 2\theta-1)=0

    ---
    Fernando Revilla
    Last edited by FernandoRevilla; November 11th 2010 at 02:19 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    8
    thanks for your answer. I thought about representing the surfaces by vectors, and got the same result.

    It leads to  (x,y,z) = {1 \over {\cos 2\theta }}\left( {\cos \theta ,\sin \theta ,1} \right) and I don't understand why this is a (straight) line. \theta is limited to  [0,\pi /4) for this curve.
    Last edited by fict; November 11th 2010 at 03:01 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Quote Originally Posted by fict View Post
    ...and I don't understand why this is a (straight) line.
    Why do you say that is a straight line?

    \theta is limited to  [0,\pi /4) for this curve.
    You need to add more values for \theta. Take into account that if  (x,y,z) belongs to the line, then:

    (-x,y,z),\;(x,-y,z),\;(-x,-y,z)

    also belong to the line.

    Regards.

    ---
    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    8
    Why do you say that is a straight line?
    In the question they asked about a line, does it mean that they refer to some general curve? not just a straight line?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersection of surfaces
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 20th 2011, 03:38 AM
  2. Intersection of two surfaces
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 2nd 2011, 04:50 AM
  3. Intersection of Surfaces
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 15th 2009, 03:25 AM
  4. Intersection of surfaces
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 16th 2009, 09:57 PM
  5. Curve of intersection with two surfaces
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 10th 2008, 10:54 PM

Search Tags


/mathhelpforum @mathhelpforum