Asymptotes
10. Equate coefficient of highest power of x and get asymptote parallel to X-axis.
11. Similarly equate coefficient of highest power of y and get asymptote parallel to Y-axis.
The Sign of( dy / dx)
Find points at which( dy / dx) vanishes or becomes infinite. It gives us the points where tangent is parallel or perpendicular to the X-axis.
Points of Inflexion
and solve the resulting equation. If some point of inflexion is there, then locate it exactly.
Taking in consideration of all above information, we draw an approximate shape of the curve.