Intercepts in quadric surfaces?

[yoohyojinn]

Intercepts in quadric surfaces??

Homework Statement

How many intercepts can an ellipsoid have?

Homework Equations

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]

Homework Statement

How many intercepts can an ellipsoid have?

Homework Equations

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.

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.

is it right??

Thanks.

 

[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]

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?

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.