  In the present paper, we will discuss the Hankel determinants $H(f)
=a_2a_4-a_3^2$ of order 2 for normalized concave functions
$f(z)=z+a_2z^2+a_3z^3+\dots$ with a pole at $p\in(0,1).$ Here, a meromorphic
function is called concave if it maps the unit disk conformally onto a domain
whose complement is convex. To this end, we will characterize the coefficient
body of order 2 for the class of analytic functions $\varphi(z)$ on $|z|<1$
with $|\varphi|<1$ and $\varphi(p)=p.$ We believe that this is helpful for
other extremal problems concerning $a_2, a_3, a_4$ for normalized concave
functions with a pole at $p.$
