Subdivision is a method of generating smooth curves or surfaces. In recent years, subdivision curves and surfaces have come to the forefront of geometric modeling. There is a variety of existing subdivision schemes whose classification can be based on different criteria. In this dissertation non-stationary subdivision schemes are de veloped using the hyperbolic form of Lagrange-like interpolant, trigonometric and hy perbolic forms of uniform B-spline. These schemes are presented mainly to overcome the limitation of generation of conics by subdivision schemes especially parabolas and hyperbolas. Asymptotic equivalence method has been used for convergence analysis of the proposed schemes. Curvature plot technique has been employed to check the accuracy and efficiency of the proposed schemes to construct conic-sections. The ge ometrical behavior of the proposed schemes has been depicted through explanatory examples.