Optimal bound vortex geometry conditions are obtained by direct variation of the induced drag functional. Problems of induced drag minimization are examined for given bound vortex length and camber (i.e., clearance limits on vertical size) as well as for given wing lift and span. Corresponding optimal geometries and circulation distributions along the bound vortex are obtained, and induced drag values for these configurations are computed. Finally, it is shown that for given lift and bound vortex length and without constraints on the wing span and length, the minimum induced drag is produced by the plane wing with an elliptical circulation distribution.