Let $X,Y$ be given as solutions to the following system of stochastic differential equations
$$ dX = aXdt - YdW \ \ X_0 = x_0\\ dY = aYdt + XdW \ \ Y_0 = y_0 $$
Where the initial values are deterministic constants. Prove that the process defined by $R(t) = X_t^2 + Y_t^2$ is deterministic.
I tried calculating $Var[R]$ in hope that it would be equal to $0$ and thus $R$ will be deterministic. But I'm stuck at $Var[R] = E[X_t^4 + 2X_t^2Y_t^2 + Y_t^4] - E[X_t^2 + Y_t^2]= ?$