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.
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.
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.
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?
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.