  We examine the implications for the distribution of extrasolar planets based
on the null results from two of the largest direct imaging surveys published to
date. Combining the measured contrast curves from 22 of the stars observed with
the VLT NACO adaptive optics system by Masciadri et al. (2005), and 48 of the
stars observed with the VLT NACO SDI and MMT SDI devices by Biller et al.
(2007) (for a total of 60 unique stars; the median star for our survey is a 30
Myr K2 star at 25 pc), we consider what distributions of planet masses and
semi-major axes can be ruled out by these data, based on Monte Carlo
simulations of planet populations. We can set this upper limit with 95%
confidence: the fraction of stars with planets with semi-major axis from 20 to
100 AU, and mass >4 M_Jup, is 20% or less. Also, with a distribution of planet
mass of dN/dM ~ M^-1.16 between 0.5-13 M_Jup, we can rule out a power-law
distribution for semi-major axis (dN/da ~ a^alpha) with index 0 and upper
cut-off of 18 AU, and index -0.5 with an upper cut-off of 48 AU. For the
distribution suggested by Cumming et al. (2007), a power-law of index -0.61, we
can place an upper limit of 75 AU on the semi-major axis distribution. At the
68% confidence level, these upper limits state that fewer than 8% of stars have
a planet of mass >4 M_Jup between 20 and 100 AU, and a power-law distribution
for semi-major axis with index 0, -0.5, and -0.61 cannot have giant planets
beyond 12, 23, and 29 AU, respectively. In general, we find that even null
results from direct imaging surveys are very powerful in constraining the
distributions of giant planets (0.5-13 M_Jup) at large separations, but more
work needs to be done to close the gap between planets that can be detected by
direct imaging, and those to which the radial velocity method is sensitive.
