  We examine the large-$N_c$ relations which express the electromagnetic
$N$-to-$\Delta$ transition quantities in terms of the electromagnetic
properties of the nucleon. These relations are based on the known large-$N_c$
relation between the $N\to \Delta$ electric quadrupole moment and the neutron
charge radius, and a newly derived large-$N_c$ relation between the electric
quadrupole ($E2$) and Coulomb quadrupole ($C2$) transitions. Extending these
relations to finite, but small, momentum transfer we find that the description
of the electromagnetic $N\to\Delta$ ratios ($R_{EM}$ and $R_{SM}$) in terms of
the nucleon form factors predicts a structure which may be ascribed to the
effect of the ``pion cloud''. These relations also provide useful constraints
for the $N \to \Delta$ generalized parton distributions.
