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Intersection of a circle with coordinate planes

  1. Jan 31, 2015 #1
    1. The problem statement, all variables and given/known data
    Find an equation of the sphere with center (2, -6, 4) and radius 5. Describe its intersection with the each of the coordinate planes.

    2. Relevant equations
    Equation of a sphere with three dimensions X2 + Y2 + Z2 = R2

    3. The attempt at a solution
    My equation is (x - 2)2 + (y + 6)2 + (z - 4)2 = 25
    This sphere intersects the XY plane by making a circle with radius 3 and it intersects the YZ plane with a radius of (21)0.5. However, my equation for the XZ plane came out to be negative. That is, Radius squared is less than zero. Does that mean the sphere doesn't intersect the XZ plane?
     
  2. jcsd
  3. Jan 31, 2015 #2

    Borg

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    Gold Member

    Since one of your starting points (-6) is farther from an axis than the radius of the sphere (5), it seems reasonable that the sphere wouldn't intersect with one of the planes.
     
  4. Feb 1, 2015 #3
    Thanks Borg. I never noticed the correlation between the points and the radius before.
     
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