Ex: Intersection of a Line and a Circle - Application

Problem Setup00:00:00

Define the problem: calculating signal coverage on a 27-mile drive between two cities relative to a transmitter located at the origin with a 10-mile radius.

Coordinate Plane Representation00:00:25

Graph the transmitter as a circle with the equation x^2 + y^2 = 100, and plot the two cities' coordinates at (-15, 5) and (12, 5).

Solving the System of Equations00:03:00

Set the line equation y = 5 into the circular equation x^2 + y^2 = 100 to find the intersection points where the signal starts and ends.

Calculating the Result00:04:33

Determine the exact signal distance is 10 times the square root of 3, providing a decimal approximation of roughly 17.32 miles.