Question

The equation (x-3)^2+(y+7)^2=64 models the position and range of the source of a radio signal. Describe the position of the source and the range of the signals.

Answer 1

`\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r}\\\\ -------------------------------\\\\ (x-3)^2+(y+7)^2=64\implies [x-\stackrel{h}{3}]^2+[y-(\stackrel{k}{-7})]^2=\stackrel{r}{8^2} \\\\\\ center~(3,-7)\qquad radius=8`

so, the broadcast location and range is more or less like the picture below.

Answer 2

This is the equation of a circle with center (3, -7)  which gives you the position of the source and the 64 is the square of the radius. So  the range of the signals is in a circle radius 8 miles from the center.