  We fit the multi-band lightcurves of 40 fast blue optical transients (FBOTs)
with the magnetar engine model. The mass of the FBOT ejecta, the initial spin
period and polar magnetic field of the FBOT magnetars are respectively
constrained to $M_{\rm{ej}}=0.18^{+0.52}_{-0.13}\,M_\odot$,
$P_{\rm{i}}=9.4^{+8.1}_{-3.9}\,{\rm{ms}}$, and $B_{\rm
p}=7^{+16}_{-5}\times10^{14}\,{\rm{G}}$. The wide distribution of the value of
$B_{\rm p}$ spreads the parameter ranges of the magnetars from superluminous
supernovae (SLSNe) to broad-line Type Ic supernovae (SNe Ic-BL; some are
observed to be associated with long-duration gamma-ray bursts), which are also
suggested to be driven by magnetars. Combining FBOTs with the other transients,
we find a strong universal anti-correlation as
$P_{\rm{i}}\propto{M_{\rm{ej}}^{-0.45}}$, indicating them could share a common
origin. To be specific, it is suspected that all of these transients originate
from collapse of extreme-stripped stars in close binary systems, but with
different progenitor masses. As a result, FBOTs distinct themselves by their
small ejecta masses with an upper limit of ${\sim}1\,M_\odot$, which leads to
an observational separation in the rise time of the lightcurves $\sim12\,{\rm
d}$. In addition, the FBOTs together with SLSNe can be separated from SNe Ic-BL
by an empirical line in the $M_{\rm peak}-t_{\rm rise}$ plane corresponding to
an energy requirement of a mass of $^{56}$Ni of $\sim0.3M_{\rm ej}$, where
$M_{\rm peak}$ is the peak absolute magnitude of the transients and $t_{\rm
rise}$ is the rise time.
