The relation $\sim$ on $R \times R$ is defined by $(a,b) \sim (c,d)$ iff $a^2 +b^2 = c^2 + d^2$.
I have already proven that this is an equivalence relation but I need to give a geometric description of the equivalence classes and I'm not sure how.
The relation $\sim$ on $R \times R$ is defined by $(a,b) \sim (c,d)$ iff $a^2 +b^2 = c^2 + d^2$.
I have already proven that this is an equivalence relation but I need to give a geometric description of the equivalence classes and I'm not sure how.
Note that $x^2+y^2=r^2$
Two points are equivalent if they are equidistant from the origin
The equivalence classes are circles that have the origin as a center
Hint: What does $x^2+y^2=r^2$ represent?