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 .