Question

one of the parking lot lights at a hospital has a motion detector on it, and the equation $(x + 10)^2+(y - 8)^2 = 16$ describes the boundary within which motion can be sensed. what is the greatest distance, in feet, a person could be from the parking lot light and be detected? 2 ft 4 ft 9 ft 256 ft

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Identify the radius from the given equation

Given the equation \((x + 10)^2+(y - 8)^2=16\). Comparing with the standard form \((x - h)^2+(y - k)^2=r^2\), we have \(r^2 = 16\).

Step3: Calculate the radius

Take the square - root of \(r^2\). Since \(r=\sqrt{r^2}\) and \(r^2 = 16\), then \(r = 4\) (we take the positive value because radius is a non - negative quantity).

Answer:

\(4\mathrm{ft}\)