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In the present paper we derive a new Hankel determinant representation forthe square of the Vorob'ev-Yablonski polynomial$\mathcal{Q}_n(x),x\in\mathbb{C}$. These polynomials are the major ingredientsin 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 thezero distribution of $\mathcal{Q}_n(x)$ as $n\rightarrow\infty$ byasymptotically analyzing a certain collection of (pseudo) orthogonalpolynomials connected to the aforementioned Hankel determinant. Our approachreproduces recently obtained results in the same context by Buckingham andMiller \cite{BM}, which used the Jimbo-Miwa Lax representation of PII equationand the asymptotical analysis thereof.

Zeros of large degree Vorob'ev-Yablonski polynomials via a Hankel determinant identity