  We prove that the zeros of ${}_2F_1(-n,\frac{n+1}{2};\frac{n+3}{2};z)$
asymptotically approach the section of the lemniscate $\{z: |z(1-z)^2|=4/27;
\textrm{Re}(z)>1/3\}$ as $n\rightarrow \infty$. In recent papers (cf.
\cite{KMF}, \cite{orive}), Mart\'inez-Finkelshtein and Kuijlaars and their
co-authors have used Riemann-Hilbert methods to derive the asymptotic zero
distribution of Jacobi polynomials $P_n^{(\alpha_n,\beta_n)}$ when the limits
$\ds A=\lim_{n\rightarrow \infty}\frac{\alpha_n}{n}$ and $\ds
B=\lim_{n\rightarrow \infty}\frac{\beta_n}{n}$ exist and lie in the interior of
certain specified regions in the $AB$-plane. Our result corresponds to one of
the transitional or boundary cases for Jacobi polynomials in the Kuijlaars
Mart\'inez-Finkelshtein classification.
