Engineering Mathematics

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,

 

 

 

 

and

 

 

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

 

EXAMPLE 11.66