Question

Solve. A power outage affected all homes and businesses within a 3 mile radius of the power station. If the power station is located 5 miles west and 6 miles north of the center of town, find an equation of the circle consisting of the furthest points from the station affected by the power outage

Answer 1

Answer:

$\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 9$

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 :

$\left ( x-a \right )^{2}+\left ( y-b \right )^{2}= r^{2}$

Hence the equation of the resulting circle will be: $\left ( x+5 \right )^{2}+\left ( y-6 \right )^{2}= 3^{2}$