Results 1 to 2 of 2

Math Help - Find the equation of a sphere

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    19

    Find the equation of a sphere

    Find an equation of the sphere that passes through points (0, -2, 2), (4, 0, 0), (-2, 1, 5), and (7, 7, 9).

    My first thought was to somehow find vectors from these points, but I'm not so sure that's the case.

    I also think this involves a gigantic matrix with its determinant being solved for, but I'm not sure how to approach it.

    On top of that, I think the midpoint rule might be involved somehow, but once again, I'm not exactly sure how to approach it without getting way off track.

    Could someone help sort my ideas out and give me some direction? I just have too many thoughts about what to do, and it's frustrating me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,392
    Thanks
    56
    Quote Originally Posted by wilcofan3 View Post
    Find an equation of the sphere that passes through points (0, -2, 2), (4, 0, 0), (-2, 1, 5), and (7, 7, 9).

    My first thought was to somehow find vectors from these points, but I'm not so sure that's the case.

    I also think this involves a gigantic matrix with its determinant being solved for, but I'm not sure how to approach it.

    On top of that, I think the midpoint rule might be involved somehow, but once again, I'm not exactly sure how to approach it without getting way off track.

    Could someone help sort my ideas out and give me some direction? I just have too many thoughts about what to do, and it's frustrating me.
    The general equation of a sphere is

    (x-a)^2+(y-b)^2+(z-c)^2 = r^2

    Substitute your 4 points into this and you'll get 4 equations for the 4 unknowns a, b, c,\, \text{and}\,r. If you substract the equations, say eqn 1 - eqn2, eqn2- eqn3, eqn3 - eqn4, you'll get three linear equations for a, b, \, \text{and}\,c which you can solve. Then use any one of the original equation to find r.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 25th 2011, 03:49 PM
  2. Replies: 16
    Last Post: January 21st 2011, 01:37 PM
  3. Replies: 1
    Last Post: November 2nd 2010, 01:49 AM
  4. Find Equation of Sphere
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: October 13th 2008, 07:31 AM
  5. find the equation of the sphere
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 27th 2007, 03:57 PM

Search Tags


/mathhelpforum @mathhelpforum