In space, the collection of all points that are the same distance from some fixed point is

Question:

In space, the collection of all points that are the same distance from some fixed point is called a sphere. See the illustration. The constant distance is called the radius, and the fixed point is the center of the sphere. Show that the equation of a sphere with center at (x₀,y₀,z₀) and radius r is

(x – x₀)² + (y – y₀)² + (z – z₀)² = r²

P = (x, y, z) Ро - (х Уб, 20) х