Question

The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation (x+14)2+(y−6)2=9 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the lamp and be detected?
3 ft

6 ft

9 ft

81 ft

Answer 1

Answer: The greatest distance, in feet is the first one 3ft.

Answer 2

Answer: 3 feet

Step-by-step explanation:

Given: The blueprints for a police station show that one of the lamp posts has a motion detector on it, and that the equation describes the boundary within which motion can be sensed. :

$(x+14)^2+(y-6)^2=9$ → which is a equation of a CIRCLE.

When we compare it to the standard form of equation of circle i.e. $(x-(-14))^2+(y-6)^2=3^2$ , we get the radius of the circle = 3

Consider the lamp post as the center of the area covered by the detector.

Then the greatest distance a person could be from the lamp and be detected = Radius of the circular area

=3 feet.