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

• Mar 25th 2011, 02:16 PM
Yehia
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!!
• Mar 25th 2011, 02:49 PM
Plato
Quote:

Originally Posted by Yehia
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 \$\displaystyle (3,5,3)\$ is the mid point between \$\displaystyle (1,4,5)~\&~(5,6,1)\$.