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Equation of sphere given 3 pointcalc 3

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the equation of a sphere that contains the points (-3,0,0) (3,4,4) and (-4,3,4) if its center lies on the xz plane


    2. Relevant equations
    Not sure...i used the distance formula though


    3. The attempt at a solution
    This class has just started and i have no idea where to start with this becuase this is our first homework!! I am trying to find a point equidistant from all three points that could be the center, but I could only find a plane which I found to be 2z+3x=4


    Please help!! I am really frustrated =(
     
  2. jcsd
  3. Sep 13, 2009 #2

    rock.freak667

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    Homework Helper

    General of a sphere

    (x-h)2+(y-j)2+(z-k)2=r2 where (h,j,k) is the centre of the sphere.

    you have three points and what plane the centre lies on
     
  4. Sep 13, 2009 #3
    This question is like an analogy to those involving simultaneous equations. ;) Try to substitute the 3 points into the general equations and solve for the unknowns.
     
  5. Sep 13, 2009 #4
    thanks, rockfreak

    lkh - what do you mean by the problems with simultaneous equations?
     
  6. Sep 13, 2009 #5
    ohhh ok thanks!!! i got it it was much simpler than i thought :)
     
  7. Sep 13, 2009 #6
    Because the center lies on the xz plane than its coordinates are (x,0,z)

    The equation would be:

    [tex](x-x_0)^2+y^2+(z-z_0)^2=r^2[/tex]
     
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