Question

The answer for Mixed Degree Systems 

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

Two distinct concentric circles: Zero

Two distinct parabolas: two

A line and a circle: two

A parabola and a circle: Four

Answer 1

we have been asked to find the maximum number of solutions each of the following systems could have?

Two distinct concentric circles: Zero

Two distinct concentric circles never intersects each other . Hence it does not have any solutions.

Two distinct parabolas: two

As we know that the two parabolas intersect at a maximum of Two Points. Hence the maximum number of solution is Two.

A line and a circle: two

A line and a circle can intersect at a maximum of Two Points. Hence the maximum number of solution is Two.

A parabola and a circle: Four

A Parabola and a circle can intersect at a maximum of Four Points. Hence the maximum number of solution is Four.

Answer 2

We have to find the maximum number of solutions of each of the following system:

1)

Two distinct concentric circles:

Since, distinct concentric circles means that the two circles have same center but different radius.

That means they will never intersect each other at any point.

Ans hence we will get zero solutions.

2)

Two distinct parabolas:

Two parabolas can maximum intersect at 2 points this could be seen by the diagrams.

3)

A line and a circle.

A line and a circle can maximum have 2 solutions.

4)

A parabola and a circle.

It can have maximum two solutions it can be seen from the diagram.