# Derive the equation of a circle

for any 3 points in space $(x_1,y_1,z_1)$, $(x_2,y_2,z_2)$, $(x_3,y_3,z_3)$, provided they are not co-linear there is a unique circle that can be drawn through these points.

What is the equation of this circle in terms of $(x_1,y_1,z_1)$, $(x_2,y_2,z_2)$, and $(x_3,y_3,z_3)$?

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Do you know how to find the equation of a circle through three given, non-collinear points on the plane? – Arturo Magidin Apr 26 '12 at 2:46
See this. – Ｊ. M. Apr 26 '12 at 2:48