In the plane, using Cartesian coordinates, a circle with radius 1 with center at the origin is described by the equation x² + y² = 1. In other words, this circle is the set of all points of the form (x, y) in the plane that satisfy the above equation. In order to describe a circle whose center is not at the origin, we can translate the axes. In other words, we move the origin to a new point say (x₀, y₀). So if (p, q) is a point with respect to the old coordinates, then it is (p + x₀, q + y₀) with respect to the new coordinates. Thus the equation for the circle in the new coordinates is (x + x₀)² + (y + y₀)² = 1. In general, if a curve is described by the equation f(x, y) = c for some function f and some real constant c, then the curve is described in the new coordinates by the equation f(x + x₀, y + y₀) = c. Translation preserves the distance between points. In other words, the distance between point (p, q) are (r, s) is the same as the distance between the points (p + x₀, q + y₀) and (r + x₀, s + y₀). These ideas extend in a natural way to n-dimensional space for any positive integer n.