A circle is centered at J(3, 3) and has a radius of 12. Where does the point F(-6,-5) lie?
Choose 1
A.- Inside the circle
B.-On the circle
C.- Outside the circle

is outside the circle of radius of centered at .

Step-by-step explanation:

Let and denote the center and the radius of this circle, respectively. Let be a point in the plane.

Let denote the Euclidean distance between point and point .

In other words, if is at while is at , then .

Point would be inside this circle if . (In other words, the distance between and the center of this circle is smaller than the radius of this circle.)

Point would be on this circle if . (In other words, the distance between and the center of this circle is exactly equal to the radius of this circle.)

Point would be outside this circle if . (In other words, the distance between and the center of this circle exceeds the radius of this circle.)

Calculate the actual distance between and :

.

On the other hand, notice that the radius of this circle, , is smaller than . Therefore, point would be outside this circle.

2.83941151 would be the answer you're looking for! : )