To find the equation of the drone's path, we can first find the coordinates of the center of the circle that the drone is flying around. We can do this by finding the midpoint between the two points the drone passes over:
Midpoint in the x-direction: (220 ft - 180 ft)/2 = 20 ft to the right of the origin.
Midpoint in the y-direction: (230 ft - 180 ft)/2 = 25 ft above the origin.
Therefore, the center of the circle is located at (20, 25) ft.
The radius of the circle can be found by calculating the distance between the center of the circle and either of the two points the drone passes over:
Radius: sqrt((20-(-180))^2 + (25-180)^2) = sqrt(40000 + 15625) = 205 ft (rounded to the nearest whole number)
So the equation for the drone's path is:
(x - 20)^2 + (y - 25)^2 = 205^2
To find how far north of Megan's position the drone is when it passes due north, we can substitute x = 0 into the equation:
(0 - 20)^2 + (y - 25)^2 = 205^2
400 + (y - 25)^2 = 42025
(y - 25)^2 = 41625
y - 25 = +/-sqrt(41625)
y = 25 +/- 204.06
So the drone is either 229.06 ft north or 22.94 ft south of Megan's position when it passes due north. Rounded to three decimal places, the answer is 229.06 ft north.