Given $\mathbb{R}^2$ with its usual topology, we define the following equivalence relations and I'm asked for the quotient spaces:
a)$(x_1,y_1)R(x_2,y_2)$ iff $x_1^2+y_1^2=x_2^2+y_2^2$
I understand that the equivalence classes are circles with center $(0,0)$, and that the quotient space here is $[0,+\infty)$ with the induced topology. To prove this I've followed the usual strategy of finding an identification.
b)$(x_1,y_1)R(x_2,y_2)$ iff $x_1^2+y_1=x_2^2+y_2$
Here I don't know how to start because I can't imagine the equivalence classes. I would appreciate any help.