  In the present paper we derive a new Hankel determinant representation for
the square of the Vorob'ev-Yablonski polynomial
$\mathcal{Q}_n(x),x\in\mathbb{C}$. These polynomials are the major ingredients
in the construction of rational solutions to the second Painlev\'e equation
$u_{xx}=xu+2u^3+\alpha$. As an application of the new identity, we study the
zero distribution of $\mathcal{Q}_n(x)$ as $n\rightarrow\infty$ by
asymptotically analyzing a certain collection of (pseudo) orthogonal
polynomials connected to the aforementioned Hankel determinant. Our approach
reproduces recently obtained results in the same context by Buckingham and
Miller \cite{BM}, which used the Jimbo-Miwa Lax representation of PII equation
and the asymptotical analysis thereof.
