We will determine if the functions represent a circle with a real non-zero radius as follows:
b)
So, we try to factor it to determine the nature of the quadratic equation and since it cannot be factored or even plotted, we will have that it is not a circle with a real non-zero radius.
c)
So, we try to factor it:
We can factor in a limited fashion, but we can conclude that it is not a circle with a non-zero radius given the nature of the factorization.