SHARYGIN 2017 Problem 20

Given a right-angled triangle $ABC$ and two perpendicular lines $x$ and $y$ passing through the vertex $A$ of its right angle. For an arbitrary point $X$ on $x$ define $y_B$ and $y_C$ as the reflections of $y$ about $XB$ and $XC$ respectively. Let $Y$ be the common point of $y_b$ and $y_c$ . Find the locus of $Y$ (when $y_b$ and $y_c$ do not coincide).