Question

a low-wattage radio station can be heard only within a certain distance from the station. on the graph below, the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. which equation represents the boundary for the region where the station can be heard,help I need the explanation for it

Answer 1

In order to find the equation that represents this boundary, let's use the equation of the circumference below:

$(x-h)^2+(y-k)^2=r^2$

Where r is the radius and the center of the circumference is the point (h, k).

Looking at the image, we can see that the circumference is centered at (-6, -1), and its radius is equal 4 units.

So we can write the following equation, using h = -6, k = -1 and r = 4:

$(x+6)^2+(y+1)^2=16$

Therefore the correct option is the second one.