Intercepts in quadric surfaces?

  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. 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. 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. 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. Re: Intercepts in quadric surfaces??

    that sounds right
     
  7. 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.
     
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