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Sphere Intersects with Plane

  1. Jan 24, 2010 #1
    I have a sphere with the equation
    (x-3)2+(y-2)2+(z+5)2=36

    two question:
    1. how do I find the equation of the shapes where the surface intersects each coordinate plane.
    2. How do I find the points where the surface intersects each coordinate axis.

    I think for 1. that it will be a circle but how do I find the equation of that circle? What part of the sphere equation do I need to set to zero?
     
  2. jcsd
  3. Jan 25, 2010 #2
    A point (x,y,z) is in both the sphere and the yz-plane iff:
    [tex](x-3)^2 + (y-2)^2 + (z+5)^2 = 36[/tex]
    [tex]x=0[/tex]
    So just substitute x=0 in the sphere equation to get a circle equation. For the intersection with the z-axis we have:
    [tex](x-3)^2 + (y-2)^2 + (z+5)^2 = 36[/tex]
    [tex]x=0[/tex]
    [tex]y=0[/tex]
     
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