  For any delta > 1 we construct a periodic and locally finite packing of the
plane with ellipses whose delta-enlargement covers the whole plane. This
answers a question of Imre B\'ar\'any. On the other hand, we show that if C is
a packing in the plane with circular discs of radius at most 1, then its
1.00001-enlargement covers no square with side length 4.
