Question

The equation of a circle is (x+4)2+(y−5)2=121.

1.) What is the center and radius of the circle?

center: (−4, 5); radius: 11
center: (−4, 5); radius: 121
center: (−4, −5); radius: 121
center: (4, −5); radius: 11



2.) One of the lamp posts at a bank has a motion detector on it, and the equation (x+15)2+(y−12)2=25 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?

5 ft
10 ft
50 ft
125 ft

3.) Jenni plots her house and yard on a computer. She determines that the circle that defines the part of the front yard that gets watered by the sprinkler is (x−9)2+(y+11)2=16.

What is the diameter, in meters, of the circular area that gets watered by the sprinkler?

4 m
8 m
16 m
32 m

Answer 1

Part 1) The equation of a circle is (x+4)²+(y−5)²=121.
What is the center and radius of the circle?

we know that
the equation of a circle is of the form
(x-h)²+(y-k)²=r²
in the problem
(x+4)²+(y−5)²=121.------> (x+4)²+(y−5)²=11²

the center (h,k) is the point (-4,5) and the radius is 11

Part 2) we have that
(x+15)²+(y−12)²=25-------> (x+15)²+(y−12)²=5²

we know that
the greatest distance, in feet, a person could be from the lamp and be detected is the radius

the radius is equal to 5 ft

the answer Part 2) is 5 ft

Part 3) we have that
(x−9)²+(y+11)²=16--------> (x−9)²+(y+11)²=4²

the radius is equal to 4 m
so the diameter is ------> 4*2-----> 8 m

the answer Part 3) is
8 m