Show that the relation R in the set A of points in a plane given by R = {(P, Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P≠(0,0) is the circle passing through P with the origin as centre.

Show that the relation R in the set A of points in a plane given by R

1.	Show that the relation R in the set A of points in a plane given by R = {(P, Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point P≠(0,0) is the circle passing through P with the origin as centre.
Answer» Show that the relation R in the set A of points in a plane given by R = {(P, Q): Distance of the point P from the origin is same as the distance of the point Q from the origin}, is an equivalence relation. Further, show that the set of all point related to a point $P \neq (0, 0)$ is the circle passing through P with the origin as centre.