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Equation of a Sphere

Vector form Let 87798.png be the position vector of the center C of the sphere and a be the radius of the sphere. Then equation of sphere is 87804.png, where 87814.png is any point on the sphere.
Cartesian form Equation of sphere is x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0, where its center is (–u, –v, –w) and radius equal 87820.png.

Diameter form of the equation of a sphere

Equation of sphere having extremities of diameter as points 87826.png is 87832.png = 0 or 87839.png = 0
Cartesian form If (x1, y1, z1) and (x2, y2, z2) are extremities of the diameter then equation of sphere is (xx1)(xx2) + (yy1) (yy2) + (zz1) (zz2) = 0

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