  The possible conditions for hadron-quark phase transition in hybrid star
cores are investigated in the present work. For the hadronic matter part the
effective chiral model is adopted. Exotic baryonic degrees like hyperons and
the delta baryons are also taken into account. As $\Delta$s posses Breit-Wigner
mass distribution ($1232 \pm 120$ MeV), the hadronic equation of state is
obtained by varying the mass of the delta baryons in this range. For the quark
phase the MIT bag model is chosen with repulsive effects of the unpaired
quarks. Phase transition is achieved using Gibbs construction and the gross
properties of the resultant hybrid star are calculated in both static and
rotating conditions and compared with the various constraints on them from
different observational and empirical perspectives. The work presents a
thorough study of the phase transition properties like the critical density of
appearance of quarks, the density range for the persistence of the mixed phase
and the population of different hadrons and quarks in hybrid star matter. The
hybrid star properties, calculated in both static and rotating conditions, are
found to be consistent with the bounds on them from different perspectives.
