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.