Editing Sphere (section)

====Pencil of spheres====
{{Main|Pencil (mathematics)#Pencil of spheres}}
If {{math|1=''f''(''x'', ''y'', ''z'') = 0}} and {{math|1=''g''(''x'', ''y'', ''z'') = 0}} are the equations of two distinct spheres then
:<math>s f(x,y,z) + t g(x,y,z) = 0</math>
is also the equation of a sphere for arbitrary values of the parameters {{mvar|s}} and {{mvar|t}}. The set of all spheres satisfying this equation is called a '''pencil of spheres''' determined by the original two spheres. In this definition a sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical plane) in the pencil.<ref name=Woods266 />