= Solution
A <quasar> is a luminous <active galactic nucleus> powered by <gas> <accretion> onto a <supermassive black hole>. The hot disc produces much of the optical/ultraviolet continuum; surrounding <gas> gives broad and narrow <emission lines>, while some systems have <relativistic jets>. A small emitting region is inferred from rapid variability, $R\lesssim c\Delta t_{\rm obs}/(1+z)$ when beaming is absent. Sustaining a high <luminosity> from such a compact region favours <accretion> over ordinary stellar power. For approximately spherical, ionized hydrogen with electron-scattering opacity,
$$
L_E=\frac{4\pi GMm_pc}{\sigma_T}\simeq1.26\times10^{31}\frac{M}{M_\odot}\,\mathrm W.
$$
Comparing <luminosity> with this Eddington scale constrains <mass> only after assumptions about anisotropy, opacity and <accretion> state. The emitted power obeys $L=\eta\dot Mc^2$; high binding-energy efficiency makes growth of a massive compact accretor energetically plausible.
Broad-line <reverberation mapping> estimates a <gas> radius from a continuum-to-line time lag, $R\sim c\tau$, and combines it with line velocity width to infer $M\sim f_{\rm vir}Rv^2/G$. Geometry, inclination and nongravitational <gas> motions enter the factor $f_{\rm vir}$. Independent evidence for compact massive nuclei comes from resolved stellar or <gas> orbits in nearby galaxies. <Andrea M. Ghez> and collaborators' Galactic-centre stellar-orbit study fitted a common central potential and <distance>, demonstrating a compact dark <mass> of order four million <solar masses>; the Galactic centre is a low-luminosity example rather than a <quasar>.<Measuring Distance and Properties of the Milky Way's Central Supermassive Black Hole with Stellar Orbits by Andrea M. Ghez and others>[abstract; joint potential/distance fits and systematic-error analysis]{ref}
\b[<quasars> are an <accretion> phase of massive nuclear <black holes>; <luminosity>, variability and dynamical evidence constrain different aspects of that interpretation.] A finite-resolution dark-mass measurement by itself is not a direct image of an <event horizon>.
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