Question

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

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