In polar oxide interfaces phenomena such as conductivity, superconductivity, magnetism, one-dimensional conductivity and Quantum Hall states can emerge at the polar discontinuity. Combining controllable ferroelectricity in such interfaces can affect the superconducting properties and shed light on the mutual effects between the polar oxide and the ferroelectric one. In addition, ferroelectric interfaces can be used in non-magnetic memory devices. Here we study the interface between the polar oxide LaAlO₃ and the ferroelectric Ca-doped SrTiO₃ by means of electrical transport combined with local imaging of the current flow using scanning SQUID. An anomalous behavior of the interface resistivity is observed at low temperatures. Using the SQUID imaging we find this behavior to originate from an intrinsic bias induced by the polar LaAlO₃ layer. This intrinsic bias combined with ferroelectricity strongly constrains the possible structural domain tiling near the interface. We suggest this intrinsic bias as a way to control and tune the initial state of ferroelectric materials. The hysteretic dependence of the normal and the superconducting state properties on gate voltage can be utilized in multifaceted controllable memory devices.