# Equation of a Sphere

**Vector form**Let be the position vector of the center

*C*of the sphere and

*a*be the radius of the sphere. Then equation of sphere is , where is any point on the sphere.

**Cartesian form**Equation of sphere is

*x*

^{2}+

*y*

^{2}+

*z*

^{2}+ 2

*ux*+ 2

*vy*+ 2

*wz*+

*d*= 0, where its center is (â€“

*u*, â€“

*v*, â€“

*w*) and radius equal .

# Diameter form of the equation of a sphere

Equation of sphere having extremities of diameter as points is = 0 or = 0

**Cartesian form**If (

*x*

_{1},

*y*

_{1},

*z*

_{1}) and (

*x*

_{2},

*y*

_{2},

*z*

_{2}) are extremities of the diameter then equation of sphere is (

*x*â€“

*x*

_{1})(

*x*â€“

*x*

_{2}) + (

*y*â€“

*y*

_{1}) (

*y*â€“

*y*

_{2}) + (

*z*â€“

*z*

_{1}) (

*z*â€“

*z*

_{2}) = 0