  A black hole embedded within a bright, optically thin emitting region
imprints a nearly circular "shadow" on its image, corresponding to the
observer's line-of-sight into the black hole. The shadow boundary depends on
the black hole's mass and spin, providing an observable signature of both
properties via high resolution images. However, standard expressions for the
shadow boundary are most naturally parametrized by Boyer-Lindquist radii rather
than by image coordinates. We explore simple, approximate parameterizations for
the shadow boundary using ellipses and a family of curves known as limacons. We
demonstrate that these curves provide excellent and efficient approximations
for all black hole spins and inclinations. In particular, we show that the two
parameters of the limacon naturally account for the three primary shadow
deformations resulting from mass and spin: size, displacement, and asymmetry.
These curves are convenient for parametric model fitting directly to
interferometric data, they reveal the degeneracies expected when estimating
black hole properties from images with practical measurement limitations, and
they provide a natural framework for parametric tests of the Kerr metric using
black hole images.
