1) Two distinct concentric circles have no solutions.
2) Two distinct parabolas have a maximum of two solutions.
3) A line and a circle have a maximum of two solutions.
4) A parabola and a circle have a maximum of two solutions.
Circles and parabolas can be described by second order polynomials, whereas lines are represented by first order polynomials. The maximum number of solutions is bounded by the maximum grade between the two polynomials.
Since circles are characterized by their radii, two distinct concentric circles have no solutions since radii are different. The rest of cases have a maximum of two solutions.
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