by yoohyojinn
 P: 5 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.
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P: 21,216
 Quote by yoohyojinn 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.
Seems reasonble to me.
 Quote by yoohyojinn And an elliptic parabaloid can have at least 1 intercept, and at most 6 intercepts.
I think that 6 is too many - I don't see how it could have more than 5 intercepts.
 Quote by yoohyojinn is it right?? Thanks.
 P: 5 oh yes, yes, yes, you are right. I was confused with visualizing it. an elliptic paraboloid can have at most 5 intercepts. thanks.
 P: 65 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?
 P: 5 that sounds right
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 Quote by alanlu 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?
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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