  In recent years, Radon type transforms that integrate functions over various
sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection
tomography, and radio tomography. In this paper, we consider the transform that
integrates a given function in $\RR^n$ over a set of solid ellipsoids of
rotation with a fixed eccentricity and foci restricted to a hyperplane.
Inversion formulas are obtained for appropriate classes of functions that are
even with respect to the hyperplane. Stability estimates, range description,
and local uniqueness results are also provided.
