Covering a convex body by its negative homothetic copies

We estimate the number and ratio of negative homothetic copies of a d-dimen sional convex body C sufficient for the covering of C. If the number of tho se copies is not very large, then our estimates are better than recent esti mates of Rogers and Zong. Particular attention is paid to the 2-dimensional case. It is proved that every planar convex body can be covered by two cop ies of ratio -4/3 ( this ratio cannot be lessened if C is a triangle).