The solution set to equations of the form X^2 + Y^2 = R^2? The boundary of a ball in a 2-dimensional, euclidean metric space? An equivalence class of Gaussian

The solution set to equations of the form X^2 + Y^2 = R^2? The boundary of a ball in a 2-dimensional, euclidean metric space? An equivalence class of Gaussian numbers based on their norms?