  The phenomena of deconfinement of hadronic matter into quark matter at high
density, relevant to hybrid star (HS) cores, is studied in the present work.
The effective chiral model describes the pure hadronic phase while for the
quark phase the MIT bag model is chosen with density dependent bag pressure.
Phase transition is achieved using Maxwell construction. The effect of
variation of the asymptotic value of the bag pressure ($B_{as}$) is analyzed
w.r.t to the mass and radius of the HSs. The presence of hyperons in the
hadronic sector also has significant effect on the choice of the value of
$B_{as}$. Both the hadronic composition and the choice of $B_{as}$
significantly affect the stability of the star. The gross structural properties
of the resultant HS are calculated in static condition and compared with the
various constraints on them from different observational and empirical
perspectives. The static properties like the maximum gravitational mass of the
HS, obtained with $B_{as}$=80 MeV fm$^{-3}$, is consistent with the limits
imposed from the observational analysis of PSR J0348+0432 and PSR J0740+6620.
The estimates of $R_{1.4}$ and $R_{1.6}$ of HSs are found to be within the
range prescribed from GW170817 analysis. Also the $M-R$ solutions of the HSs
are in excellent agreement with the recently obtained NICER data for PSR
J0030+0451. The results of maximum surface redshift, obtained with hybrid
equation of state, satisfy the constraints from 1E 1207.4-5209 and RX
J0720.4-3125. The work is also extended to obtain the tidal deformation
properties of the HSs. The obtained value of $\Lambda_{1.4}$ is consistent with
the bound obtained from GW170817 data analysis.
