Results 1 to 5 of 5

Math Help - Sketching Surfaces (Quick and Easy Question)

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    144

    Question Sketching Surfaces (Quick and Easy Question)

    Why is that,

     x= \sqrt{y^2 + z^2}

    Is a single cone while,

     x^2 = 9y^2 + z^2

    consists of 2 cones, tip to tip?

    I know that the second surface consists of elliptical cones, but I don't see how that could make any difference.

    How come for,

     x= \sqrt{y^2 + z^2}

    my solutions manual only shows one cone? Couldn't I rewrite this as,

     x^{2} = y^{2} + z^{2}

    Certainly there are negative values of x that will satisfy this equation as well, right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2010
    From
    Beijing, China
    Posts
    293
    Thanks
    23
    right (0,0,0) is the vertex of the cone. And {x<0} is another branch of the second cone.
    While for the first one only the {x>0} branch is allowed.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2010
    Posts
    144
    Quote Originally Posted by xxp9 View Post
    right (0,0,0) is the vertex of the cone. And {x<0} is another branch of the second cone.
    While for the first one only the {x>0} branch is allowed.
    I can see that for the first one only x>0 is allowed, but why?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,977
    Thanks
    1121
    Quote Originally Posted by jegues View Post
    I can see that for the first one only x>0 is allowed, but why?
    Becaues for real numbers, all functions are single valued. \sqrt{a} is defined as the non-negative number x such that x^2= a. \sqrt{4}= 2, not -2. Square roots are always non-negative.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Jan 2010
    Posts
    144
    Quote Originally Posted by HallsofIvy View Post
    Becaues for real numbers, all functions are single valued. \sqrt{a} is defined as the non-negative number x such that x^2= a. \sqrt{4}= 2, not -2. Square roots are always non-negative.
    In which case or scenario do we end up seeing the plus or minus case then?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quick easy question im sure
    Posted in the Algebra Forum
    Replies: 6
    Last Post: January 26th 2010, 04:50 AM
  2. Help with Sketching Surfaces in Space
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 17th 2009, 05:07 PM
  3. Quick easy question.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 18th 2009, 12:09 PM
  4. Quick Easy Question?
    Posted in the Calculus Forum
    Replies: 4
    Last Post: January 27th 2009, 09:21 AM
  5. Sketching Quadric Surfaces
    Posted in the Calculus Forum
    Replies: 7
    Last Post: September 25th 2008, 10:27 AM

Search Tags


/mathhelpforum @mathhelpforum