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

Let the origin be 0
`R=\{(P, Q):|0 P|=|0 Q|\}`
`(P, P) \in R \Rightarrow|0 p|=|0 p|` which is true



hence `R` is reflexive
$$
\begin{aligned}
&(P, Q) \in R=|0 \mathrm{P}|=|0 \mathrm{Q}| \\
...