Answer:
[tex](x-6)^{2}+(y+16)^{2}=6,400[/tex]
Step-by-step explanation:
we know that
The equation of a circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
In this problem we have
The center of the radio tower (position) is the point [tex](6,-16)[/tex]
The radius of the radio tower (range) is [tex]r=80\ miles[/tex]
substitute
[tex](x-6)^{2}+(y+16)^{2}=80^{2}[/tex]
[tex](x-6)^{2}+(y+16)^{2}=6,400[/tex]
