  We consider the problem of determining a small elliptical conductivity
anomaly in a unit disc from boundary measurements. The conductivity of the
anomaly is assumed to be a small perturbation from the constant background. A
measurement of voltage across two point-electrodes on the boundary through
which a constant current is passed. We further assume the limiting case when
the distance between two electrodes go to zero, creating a dipole field. We
show that three such measurements suffice to locate the anomaly size and
location inside the disc. Two further measurements are needed to obtain the
aspect ratio and the orientation of the ellipse. The investigation includes the
studies of the stability of the inverse problem and optimal experiment design.
