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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Mentor
 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.
 oh yes, yes, yes, you are right. I was confused with visualizing it. an elliptic paraboloid can have at most 5 intercepts. thanks.