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Cartesian Curve Tracing
Jay,
posted 2 months 1 week ago.

In order to trace the Cartesian curve it is convenient to observe the following steps:
Step 1 : Symmetry
   (a) Symmetry about the x-axis :
         Can be checked by replacing y by -y.
   (b) Symmetry about the y-axis :
          Can be checked by replacing x by -x.
   (c) Symmetry about both x and y axis:                     If powers of x and y both are even everywhere in equation.
   (d) Symmetry in the opposite quadrant :  If there is no change in equation when x is replaced by -x and y is replaced by -y simultaneously.
   (e) Symmetry about the line y=x :
         If there is no change in equation when x and y are interchanged.