Symmetry

A plane curve is Symmetric about,

i)about y-axis,if is replaced by -x and produces an equivalent equation.

 such as  given a equation  y=x^2
                                       or y=(-x)^2
                                       so y=x^2

                     so its symmetric about y-axis.


ii)about x-axis,if is replaced by -y and produces an equivalent equation.

such as  given a equation x=y^2
                                     or x=(-y)^2
                                     so x=y^2
 
                  so its symmetric about x-axis.


iii)about the origin,if and only if replacing both x by -x and y by -y in its equation produces an equivalent equation

such as  given a equation  y=x^3
                                    or -y=(-x)^3
                                    or -y=-x^3
                                    so  y=x^3
   
                 so its symmetric about origin.