  We explore the connection between supports of equilibrium measures and
quadrature identities, especially in the case of point sources added to the
external field $Q(z)=|z|^{2p}$ with $p \in \mathbb{N}$. Along the way, we
describe some quadrature domains with respect to weighted area measure
$|z|^{2p}dA_z$ and complex boundary measure $|z|^{-2p}dz$.
