Question

Noa flies a drone in a circular path around an object that is 210 meters west and 150 meters south of her

position. The drone's path takes it over a point that is 170 meters east and 190 meters north of her.

Find an equation for the drone's path. (Assume Noa is located at the origin, with the horizontal axis running
east-west and the vertical axis running north-south)

The drone's path follows the equation________

When the drone passes due north of Noa's position, it will be ___________ feet north of
her (round your answer to three decimal places).

Answer 1

We can solve this problem using the standard equation of a circle:

(x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and r is the radius.

Since Noa is at the origin, the center of the circle is the midpoint between the object and the point where the drone passes:

h = (210 - 170)/2 = 20

k = (190 - 150)/2 = 20

The radius is the distance between the center and the point where the drone passes:

r = √((170 - 20)² + (190 - 20)²) = √(150² + 170²) = √(62500) = 250

So the equation of the drone's path is:

(x - 20)² + (y - 20)² = 250²

When the drone passes due north of Noa's position, its x-coordinate is 20, so we can substitute that into the equation:

(20 - 20)² + (y - 20)² = 250²

y - 20 = ±√(250²)

y = 20 ± 250

y ≈ -230 or y ≈ 270

So the drone will be approximately 230 feet north of Noa's position.