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Intercepts in quadric surfaces? 
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#1
Feb2712, 10:16 PM

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. 


#2
Feb2812, 10:04 AM

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#3
Feb2812, 10:04 PM

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. 


#4
Feb2812, 10:22 PM

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?



#5
Feb2912, 12:23 AM

P: 5

that sounds right



#6
Feb2912, 10:12 AM

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