Intercepts in quadric surfaces??

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.

And an elliptic parabaloid can have at least 1 intercept, and at most 6 intercepts.

is it right??

Thanks.

Mark44

Seems reasonble to me.
I think that 6 is too many - I don't see how it could have more than 5 intercepts.

yoohyojinn

oh yes, yes, yes, you are right.

I was confused with visualizing it.

an elliptic paraboloid can have at most 5 intercepts.

thanks.

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?

yoohyojinn

that sounds right

Mark44

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.