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Math Help - To find a sphere's equation given two points on it and a line containing it's centre.

  1. #1
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    To find a sphere's equation given two points on it and a line containing it's centre.

    So given that a sphere (in Euclidian 3d geometry) passes through A(1,4,5) and B(5,6,1) and given the line r contains the sphere's centre and that the line is equidistant from A and B, how can you find the equation of the smallest sphere? (sphere of minimal radius).

    r = (1 + m)i + (3 + 2m)j + (0 + 2m)k

    (where m is a parameter, no lamda's on this keyboard :P)



    help very appreciated!!! thank you!!
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  2. #2
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    Quote Originally Posted by Yehia View Post
    So given that a sphere (in Euclidian 3d geometry) passes through A(1,4,5) and B(5,6,1) and given the line r contains the sphere's centre and that the line is equidistant from A and B, how can you find the equation of the smallest sphere? (sphere of minimal radius).
    The point (3,5,3) is the mid point between (1,4,5)~\&~(5,6,1).
    That is your centre. What is the radius?
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