  We propose a relativistic model of hybrid star admitting conformal symmetry
considering quark matter and baryonic matter as two different fluids. We define
interaction equations between the normal baryonic matter and the quark matter
and study the physical situations for repulsive, attractive and zero
interaction between the constituent matters. From the interaction equations we
find out the value of the equation of state (EOS) parameter for normal baryonic
matter which is found to be consistent with the value obtained from the Walecka
model for nucleonic matter at high density. The measured value of the Bag
constant is used to explore the space time geometry inside the star. The
theoretical mass-radius values are compared with the available observational
data of the compact objects. From the nature of the match with the
observational data, we predict the nature of interaction that must be present
inside the hybrid stars
