Answer:
[tex]\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 9[/tex]
Step-by-step explanation:
The power station is located 5 miles west and 6 miles north of the center of town. So if we try to locate the above points on a Cartesian plane. The co-ordinates of these points will be (-5,6).
And it is also mentioned that a power outage affected all homes and businesses within a 3 mile radius of the power station. So if we plot all the furthest points from the station affected by the power outage it will be a circle of radius 3 miles and center at (-5,6).
The equation of a circle with center (a,b) and radius r is given by :
[tex]\left ( x-a \right )^{2}+\left ( y-b \right )^{2}= r^{2}[/tex]
Hence the equation of the resulting circle will be: [tex]\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 3^{2}[/tex]
