Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Intercepts in quadric surfaces?

  1. Feb 27, 2012 #1
    Intercepts in quadric surfaces??

    1. The problem statement, all variables and given/known data

    How many intercepts can an ellipsoid have?

    2. Relevant equations



    3. The attempt at a solution


    First of all, I don't understand what exactly "an intercept" means in quadric surfaces.

    in two dimensions, intercepts are the points that the graph meets with x&y axes.

    So in three dimensions, do intercepts still mean the points that the surface meets with x,y,z axes?

    if what I understand is right, an ellipsoid can have at least 0 intercept, and at most 6 intercepts.

    And an elliptic parabaloid can have at least 1 intercept, and at most 6 intercepts.

    is it right??

    Thanks.
     
  2. jcsd
  3. Feb 28, 2012 #2

    Mark44

    Staff: Mentor

    Re: Intercepts in quadric surfaces??

    Seems reasonble to me.
    I think that 6 is too many - I don't see how it could have more than 5 intercepts.
     
  4. Feb 28, 2012 #3
    Re: Intercepts in quadric surfaces??

    oh yes, yes, yes, you are right.

    I was confused with visualizing it.

    an elliptic paraboloid can have at most 5 intercepts.

    thanks.
     
  5. Feb 28, 2012 #4
    Re: Intercepts in quadric surfaces??

    What if it was an elliptic paraboloid which was rotated so that its axis of revolution was not parallel to an axis? Couldn't it then achieve 6 intercepts?
     
  6. Feb 29, 2012 #5
    Re: Intercepts in quadric surfaces??

    that sounds right
     
  7. Feb 29, 2012 #6

    Mark44

    Staff: Mentor

    Re: Intercepts in quadric surfaces??

    I thought about that possibility (briefly), but it didn't seem to make a difference. If you spend more time at it than I did, you might be able to come up with a scenario in which there are 6 intercepts for the paraboloid.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Intercepts in quadric surfaces?
  1. Quadric surfaces (Replies: 1)

Loading...