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Find equation of sphere

  1. Feb 28, 2007 #1
    1. The problem statement, all variables and given/known data

    Find an equation of the sphere one of whose diameters has (1, 3, -5) and
    (3, -1, 3) as its endpoints.

    2. Relevant equations

    midpoint.

    3. The attempt at a solution

    i don't understand how to find the midpoint, even though its the mean of:
    (2, 1, 1)

    i've also been given the hint to find the measurement of a great circle:
    sqrt( 4 + 16 + 64 ) = sqrt(80)


    which equals: Thus,
    (x-2) ^ 2 + (y-1) ^ 2 + (z-1) ^ 2 = 80

    please help me solve this problem, i almost got it!
     
  2. jcsd
  3. Feb 28, 2007 #2

    dextercioby

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    I think the center's at (2,1,-1) and from here it follows that the radius is [itex] \sqrt{21} [/itex]
     
  4. Feb 28, 2007 #3
    sqrt( 4 + 16 + 64 ) = sqrt(80)?

    Shouldn't it be sqrt( 4 + 16 + 64 ) = sqrt(84)
     
  5. Feb 28, 2007 #4

    HallsofIvy

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    Staff Emeritus
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    The midpoint of the line segment from (x0,y0,z0) to (x1,y1,z1) is
    [tex]\left(\frac{x_0+x_1}{2},\frac{y_0+y_1}{2},\frac{z_0+z_1}{2}\right)[/tex]
    I thought everyone knew that!
    The length of the diameter is [itex]\sqrt{84}= 2\sqrt{21}[/itex].
    The length of the radius is half that: [itex]\sqrt{21}[/itex]
     
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