What does the ellipse tell me?

[annoymage]

Homework Statement

intersection x^2+y^2+z^2=4 and plane y=z

Homework Equations

n/a

The Attempt at a Solution

so, i solve it simultaneously, and get the equation of ellipse x^2+2y^2=4. but what does the ellipse tell me? is that the points of the intersection?, but aren't it should be a circle?

 

[schlynn]

First, that's not the equation for an elipse. I would be ((x^2)/4)+((y^2)/2)=1. Then set y=0 to find the intercepts. You can use the first equation you found to do that easily, you'll get \pm2.

 

[lanedance]

the first equation is the equation for a sphere of radius 2, and any plane thorugh the origin will intersect it in a circle

after substituting y=z, the equation you get is that of an ellipse projected onto the xy plane, but remember you have the extra z coordinate, so in the y=z plane it is still a circle

 

[schlynn]

Yeah, that's right, but the method he did still works. Just the substitution changes things. Checked on wolframalpha and it is x=\pm2

 

[lanedance]

why do you get 2 points? it should be the equation of a circle shouldn't it?

 

[annoymage]

i messed up, don't have basics on geometry, maybe i should read first some on plane and sphere. later i show my work

 

[lanedance]

i think what you did is ok, just missed a bit on interpretation at the end