a) A line can intersect a parabola at 2 points, 1 point, or no points respectively. The only possible way at which it intersects at 1 point, would be if it were tangent to the parabola. [Check first attachment]
b) Two different parabolas can intersect at 2 points, 1 point or no points respectively. [Check second attachment]
It is possible for 2 parabolas to intersect at 4 and even 3 points. But one of the parabolas would be on it's side. You can consider those cases.
