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Intercepts in quadric surfaces?

by yoohyojinn
Tags: intercepts, quadric, surfaces
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yoohyojinn
#1
Feb27-12, 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.
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Mark44
#2
Feb28-12, 10:04 AM
Mentor
P: 21,214
Quote Quote by yoohyojinn View Post
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.
Seems reasonble to me.
Quote Quote by yoohyojinn View Post

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.
Quote Quote by yoohyojinn View Post

is it right??

Thanks.
yoohyojinn
#3
Feb28-12, 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.

alanlu
#4
Feb28-12, 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?
yoohyojinn
#5
Feb29-12, 12:23 AM
P: 5
that sounds right
Mark44
#6
Feb29-12, 10:12 AM
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P: 21,214
Quote Quote by alanlu View Post
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.


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