  In this paper, we study the root distribution of some univariate polynomials
satisfying a recurrence of order two with linear polynomial coefficients. We
show that the set of non-isolated limits of zeros of the polynomials is either
an arc, or a circle, or a "lollipop", or an interval. As an application, we
discover a sufficient and necessary condition for the universal real-rootedness
of the polynomials, subject to certain sign condition on the coefficients of
the recurrence. Moreover, we obtain the sharp bound for all the zeros when they
are real.
