Simplifying the question, x+y^2 = (x+y^2)^2; 1=x+y^2
Using (a) x=y^2, on the above equation
we get 1=2y^2 or y^2 = 1/2, this give only one answer y=1/Sqrt(2)
For (b) xy^2=0,
Multiply 1=x+y^2 on both sides by y^2
This gives, y^2=xy^2+y^4 which translates to y^2=y^4 ie y^2=1
Now y can be +1 or -1
Therefore, answer choice should be A