Consider a coordinate system $\cal{C}$ such that the concentric half circles around two fixed points $P_1,P_2$ in the plane above line $P_1P_2$ create the grid. So any point in the upper half plane in this coordinate system looks like $(r,s)$ where $r$ and $s$ are the radius of circle around $P_1,P_2$ respectively.
Consider an arbitrary point in $\cal{C}$ be $(r_1,s_1)$. Consider this point as the origin of upper half of a Cartesian coordinate with $x$-axis parallel to the line $P_1P_2$. Let $(a,b)$ be any point in this Cartesian coordinate system and $(r_2,s_2)$ be the corresponding point in $\cal{C}$. Determine $r_2-r_1$ and $s_2-s_1$ in terms of $a$ and $b$.
Can anyone please help me with this?
Thanks