Chapter 7.1, Problem 62E

Solution

To choose: The incorrect option from the following options.

A. 0

B. 1

C. 2

D. 3

E. 5

The incorrect option is (e).

Given Information:

The statement is “the number of solution of a system of two equations in two variables, whose graphs are a circle and a parabola.”

Explanation:

Consider the given information,

Try to imagine all possible systems consisting of a circle and a parabola and the respective possible points of intersection.

As shown in the graph, the circle is kept in a fixed position as the parabola moves, indicating the possible circle−parabola configuration within the system.

  

So there is no solution, so the option (a) is correct.

And,

  

So there is 1 solution, so the option (b) is correct.

And,

  

So there is 2 solution, so the option (c) is correct.

And,

  

So there is 3 solution, so the option (d) is correct.

And,

  

So there is 4 solution, which is the maximum number of solution for the given condition. So, the option (e) is incorrect.

Therefore, the required option is (e).