  The mass of massive black holes in quasar cores can be deduced using the
typical velocities of Hb-emitting clouds in the Broad Line Region (BLR) and the
size of this region. However, this estimate depends on various assumptions and
is susceptible to large systematic errors. The Hb-deduced black hole mass in a
sample of 14 bright quasars is found here to correlate with the quasar host
galaxy luminosity, as determined with the Hubble Space Telescope (HST). This
correlation is similar to the black hole mass vs. bulge luminosity correlation
found by Magorrian et al. in a sample of 32 nearby normal galaxies. The
similarity of the two correlations is remarkable since the two samples involve
apparently different types of objects and since the black hole mass estimates
in quasars and in nearby galaxies are based on very different methods.
  This similarity provides a ``calibration'' of the Hb-deduced black hole mass
estimate, suggesting it is accurate to +-0.5 on log scale. The similarity of
the two correlations also suggests that quasars reside in otherwise normal
galaxies, and that the luminosity of quasar hosts can be estimated to +-0.5 mag
based on the quasar continuum luminosity and the Hb line width. Future imaging
observations of additional broad-line active galaxies with the HST are required
in order to explore the extent, slope, and scatter of the black hole mass vs.
host bulge luminosity correlation in active galaxies.
