Exercise 11

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