a)
This is symmetric in the y-axis as you can replace x with -x and still have the same equation.
It is also symmetric in the x-axis as you can replace y with -y and still have the same equation.
It is symmetric in the line y=x as you can replace x with y and y with x and still have the same equation.
It is symmetric in the line y=-x as you can replace x with -y and y with -x and still have the same equation.
This is symmetric with a roation by 90 degrees as you can replace x with y and y with -x and still have the same equation.
Hence by extension it is also symmetric if rotated by 180 or -90 degrees too.
So this equation has 4 axes of mirror symmetry and has a 4-fold rotational symmetry.
b) This is symmetric with a rotation by 180 as you can replace x with -x and y with -y and still have the same equation.
None of the other symmetries mentioned above work for this equation.
This equation only has a 2-fold rotational symmetry.
