1. Feb 27, 2012

### 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.

2. Feb 28, 2012

### Staff: Mentor

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

3. Feb 28, 2012

### yoohyojinn

oh yes, yes, yes, you are right.

I was confused with visualizing it.

an elliptic paraboloid can have at most 5 intercepts.

thanks.

4. Feb 28, 2012

### 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?

5. Feb 29, 2012

### yoohyojinn

that sounds right

6. Feb 29, 2012