R={(P,Q): distance of point P from the origin is the same as the distance of point Q from the origin }Clearly, (P,P)∈R since the distance of point P from the origin is always the same as the distance of the same point P from the origin.R is reflexive.Now,⇒ The distance of point P from the origin is the same as the distance of point Q from the origin.⇒ The distance of point Q from the origin is the same as the distance of point P from the origin.⇒(Q,P)∈R: R is symmetric.Now,Let (P,Q),(Q,S)∈R⇒ The distance of points P and Q from the origin is the same and also, the distance of points Q and S from the origin is the same.⇒ The distance of points P and S from the origin is the same.⇒(P,S)∈R:R is transitive.Therefore, R is an equivalence relation.The set of all points related to P=(0,0) will be those points whose distance from the origin is the same as the distance of point P from the origin.In other words, if O(0,0) is the origin and OP=k, then the set of all points related to P is at a distance of k from the origin.Hence, this set of points forms a circle with the centre as the origin and this circle passes through point P.