Question

What is the maximum number of solutions each of the following systems could have?

Answer 1

Answer:

0,2,2,4

Step-by-step explanation:

Answer 2

Answer:

Two distinct concentric circles: 0 max solutions

Two distinct parabolas: 4 max solutions

A line and a circle: 2 max solution

A parabola and a circle: 4 max solutions

Step-by-step explanation:

Two distinct concentric circles:

The maximum number of solutions (intersections points) 2 distinct circles can have is 0. You can see an example of it in the first picture attached. The two circles are shown side to side for clarity, but when they will be concentric, they will have same center and they will be superimposed. So there can be ZERO max solutions for that.

Two distinct parabolas:

The maximum solutions (intersection points) 2 distinct parabolas can have is 4. This is shown in the second picture attached. This occurs when two parabolas and in perpendicular orientation to each other.

A line and a circle:

The maximum solutions (intersection points) a line and a circle can have is 2. See an example in the third picture attached.

A parabola and a circle:

The maximum solutions (intersection points) a parabola and a circle can have is 4. If the parabola is compressed enough than the diameter of the circle, there can be max 4 intersection points. See the fourth picture attached as an example.