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Homework Help: What does the ellipse tell me?

  1. Aug 29, 2010 #1
    1. The problem statement, all variables and given/known data

    intersection [tex]x^2+y^2+z^2=4[/tex] and plane [tex]y=z[/tex]

    2. Relevant equations

    n/a

    3. The attempt at a solution

    so, i solve it simultaneously, and get the equation of ellipse [tex]x^2+2y^2=4[/tex]. but what does the ellipse tell me? is that the points of the intersection?, but aren't it should be a circle?
     
  2. jcsd
  3. Aug 29, 2010 #2
    Re: geometry

    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 [tex]\pm[/tex]2.
     
  4. Aug 29, 2010 #3

    lanedance

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    Re: geometry

    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
     
  5. Aug 29, 2010 #4
    Re: geometry

    Yeah, that's right, but the method he did still works. Just the substitution changes things. Checked on wolframalpha and it is x=[tex]\pm[/tex]2
     
  6. Aug 29, 2010 #5

    lanedance

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    Re: geometry

    why do you get 2 points? it should be the equation of a circle shouldn't it?
     
  7. Aug 29, 2010 #6
    Re: geometry

    i messed up, don't have basics on geometry, maybe i should read first some on plane and sphere. later i show my work
     
  8. Aug 29, 2010 #7

    lanedance

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    Re: geometry

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