11.21 EQUATION OF A SPHERE PASSING THROUGH FOUR POINTS

Let the equation of the sphere be

 

x2 + y2 + z2 + 2gx + 2fy + 2hz + c = 0.   (1)

 

Let this sphere pass through four points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3), and (x4, y4, z4). Thus,

 

image

 

image

 

image

 

and

 

image

 

Eliminating g, f, h, and c from (1), (2), (3), and (4), we get

 

EXAMPLE 11.66

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