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.

47

step-by-step explanation:

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is