The locus of a moving point in space such that its distance from a fixed point is constant is called a sphere. The fixed point is called the centre of the sphere. The constant distance is called the radius.
Let P(x, y, z) be any point on the sphere. Let C(a, b, c) be the centre.
This is the equation of the required sphere.
Show that the equation x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0 always represents a sphere. Find its centre ...