What is the maximum number of intersection points a parabola and a circle could have?

a. 4
b. 2
c. 1
d. 3

The correct option is A.

Step-by-step explanation:

A parabola and a circle can intersect each other at most 4 times. It can be proved through an example.

Let the equation of a parabola is

and equation of a circle is

From the below figure it is clear that the parabola and circle intersect each other at four point. From the above example it is clear that a parabola and a circle can intersect each other at most 4 times.

Therefore the correct option is A.