An equivalence relation $\rho$ on $\mathbb R^2$

Question

Define an equivalence relation $\rho$ on $\mathbb R^2$ by $(x_1,y_1)\rho(x_2,y_2)$ iff $x_1^2+y_1^2=x_2^2+y_2^2$

Then find the corresponding quotient space $\mathbb R^2/ \rho.$

Answer 1

You are correct that the equivalence classes consist of concentric circles about the origin, since $x^2 + y^2 = r^2$, each equivalence class contains all points on a given circle of radius $r$. Now, can you determine the quotient space, given each equivalence class can be identified by a single value $r \in \mathbb R, r\geq 0$?