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.