$A,B,C,D\in\mathbb R^2$, $A=(-1,0),D=(1,0)$, $AB, BC,CD$ has constant length, what is the locus of segment $BC$

Question

Denote points $A=(-1,0),D=(1,0)$, and lengths $|AB|=u$, $BC=v$, $CD=w$, where $u,v,w$ are fixed constant.

Consider $E=$ the locus of the segment $BC$, it form a subset of $\mathbb R^2$ (possibly an empty set). Can we have the explicit expression of its boundary $\partial E$?