1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    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

    User Avatar
    Homework Helper

    Re: geometry

    i think what you did is ok, just missed a bit on interpretation at the end
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook