A uniform steel beam of mass $M$ kilograms and length $2a$ metres is held in a horizontal position of equilibrium by two hydraulic supports at points $A$ and $B$. Support $A$ is located at a distance $y$ metres from the left-hand end of the beam. Support $B$ is located at a distance $(y+0.24)$ metres from the right-hand end of the beam. The magnitude of the normal reaction force exerted on the beam by the support at $B$ is four times the magnitude of the normal reaction force exerted by the support at $A$. Show that $a-y=c$, where $c$ is a constant to be determined.