  We derive the exact density profile of a harmonically trapped Bose-Einstein
condensate (BEC) which has dipole-dipole interactions as well as the usual
s-wave contact interaction, in the Thomas-Fermi limit. Remarkably, despite the
non-local anisotropic nature of the dipolar interaction, the density turns out
to be an inverted parabola, just as in the pure s-wave case, but with a
modified aspect ratio. The ``scaling'' solution approach of Kagan, Surkov, and
Shlyapnikov [Phys. Rev. A 54, 1753 (1996)] and Castin and Dum [Phys. Rev. Lett.
77}, 5315 (1996)] for a BEC in a time-dependent trap can therefore be applied
to a dipolar BEC, and we use it to obtain the exact monopole and quadrupole
shape oscillation frequencies.
