Sphere

  • The set of all points in 3 dimensional space which are at a fixed distance r from a fixed point A(a,b,c) is a sphere. The center of the sphere is A and the radius is r.

  • The equation of the sphere is (x - a)2 + (y - b)2 + (z - c)2 = r2.

  • The general equation of the sphere is x2 + y2 + z2 + 2ux + 2vy + 2wz + d = 0. Its center is (-u, -v, -w) and radius is √(u2 + v2 + w2 -d). The equation is a equation of a real sphere if (u2 + v2 + w2 -d) ≥ 0

  • The equation of a sphere passing through two points (x - x1)(x - x2) + ((y - y1)(y - y2) + (z - z1)(z - z2) = 0




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