Show that the relation `R` on 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 points related to a point `P!=(0,\ 0)` is the circle passing through `P` with origin as centre.

Explanation

`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) in 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,
Let `(P, Q) in R.`


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