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Multivariable Calculus~Equation of a Sphere

  1. Sep 9, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the Equation of the sphere with points P such that the distance from P to A is twice the distance from P to B.

    A(-2, 4, 2), B(4, 3, -1)


    2. Relevant equations

    The equation of a sphere would probably be the most relevant equation.

    That is (x-h)^2 + (y-k)^2 +(z-l)^2 = r^2



    3. The attempt at a solution

    So the way I look at it, I figure that I have to set up an equality. Therefore d(PA) = 2d(PB). I'm assuming that since point p isn't given, it is P(x, y, z)? I don't know though. If that's the case, my equation should look something like

    (x-2)^2 +(y-4)^2 +(z-2)^2 = 2((x-4)^2 +(y-3)^2 +(z+1)^2). But I'm not sure if I'm approaching the problem the right way. And I don't where to look for the radius. Any input would be appreciated! :)
     
  2. jcsd
  3. Sep 9, 2010 #2

    rock.freak667

    User Avatar
    Homework Helper

    I believe you are approaching it correctly, but that '2' would be converted to a '4' when you square both sides.

    Distance =√[(x-x1)2+(y-y1)2+(z-z1)2]


    So just expand out your equation, collect the like terms and then complete the square for each variable again.
     
  4. Sep 9, 2010 #3
    Ohhhh. Nice thanks a bunch! I hate stupid numerical mistakes like that.
     
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