# 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 x2 + y2 + z2 + 2ux + 2vy + 2wz + 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 (x1, y1, z1) and (x2, y2, z2) are extremities of the diameter then equation of sphere is (x â€“ x1)(x â€“ x2) + (y â€“ y1) (y â€“ y2) + (z â€“ z1) (z â€“ z2) = 0