<p>With the integration of large-scale renewable energy, distribution networks are experiencing operational safety problems due to its uncertainty and intermittence. Accurate evaluation of the hosting capacity in distribution networks is essential for accommodating renewable energy without violating operational constraints. In contrast to the traditional method that obtains the maximum total capacity while ignoring the coupling of the integrated renewable energy, this paper proposes a feasible region evaluation method to determine every operation point of each renewable generator to improve the evaluation accuracy. The operational constraints and related operational costs of the distribution network are used to identify the hosting capacity of renewable energy. Operational constraints, including power balance equations, capacity limits, and ramp rate constraints, are transformed into a feasible region constrained by a set of renewable energy constraints based on multi-parametric programming accounting for renewable energy coupling. The feasible region of the renewable energy hosting capacity is further quantified and visualized with the demand response, providing actionable insights for grid operators. Besides, the operational cost of feasible points is formulated by piecewise linear functions related to renewable energy outputs, promoting cost-effective economic dispatching decisions. Numerical tests show that the proposed method can accurately calculate the feasible region of the renewable energy hosting capacity and mapping costs within 1 s and the results are almost consistent with the Monte Carlo method. The tests further demonstrate that it is crucial to consider the demand response in hosting capacity evaluation of renewable energy.</p>