Question

A drone flies in a circular path around an object that is 100 feet east and 50 feet north of the drone operator. The drone's path takes it over a point that is 40 feet east and 30 feet south of the drone operator. Find an equation for the drone's path. Does the drone cross a north-south line through the operator's position? If so, where? If not, explain why. Suppose the drone operator is facing the object. Is the drone ever "behind" the drone operator? Why/why not?

Answer 1

See below

Explanation:

Let's plot the points for visibility

• Operator position is origin (0, 0)

• Drone passes through points:

• (100, 50) and (40, -30)

The path makes a line. The equation in slope-intercept form:

• y = mx + b

Slope:

• m = (-30 - 50)/(40-100) = -80/-60 = 4/3

y -intercept:

• 50 = 4/3*100 + b
• b = 50 - 400/3 = - 250/3

The equation:

• y = 4/3x - 250/3

Questions:

Does the drone cross a north-south line through the operator's position?

• No, as y-intercept is not zero. See attached

Suppose the drone operator is facing the object. Is the drone ever "behind" the drone operator?

• No. See attached