  We establish a functional identity for Mahler measures of the two-parametric
family $P_{a,c}(x,y)=a(x+1/x)+y+1/y+c$. Our result extends an identity proven
in a paper of Lal\'{i}n, Zudilin and Samart. As a by-product, we obtain
evaluations of $m(P_{a,c})$ for some algebraic values of $a$ and $c$ in terms
of special values of $L$-functions and logarithms. We also give a sufficient
condition for validity of a certain identity between the elliptic integrals of
the first and the third kind, which implies several identities for
$m(P_{a,c})$.
