1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook