In this paper, an important novel study with interesting conclusions on algebraic cubic curves and elliptic curves is being presented. Various popular algebraic cubic curves and elliptic curves viz., Ochoa curve, Mordell curve, projection, birational transformation, Conchoid of de Sluze, Maltese cross curve, Semicubical Parabola, Tschirnhausen Cubic, Right Strophoid, Strophoid, have been studied.

The paper has three novelties - different curves obtained by changing coefficients, the solutions in both  x  and y are given and the roots which are obtained from the algebraic curve equation,are again interpolated with different degrees viz., degree 2, 4, 6 and 10, with root mean square error.

Many accomplished graduates, mathematicians or scientists, will question its need. But interesing results are found, which are given in the conclusion.