# Question #d744c

Mar 10, 2017

$5$ feet.

#### Explanation:

Let's assume that the equation describes the distances in feet.

So, the graph of ${\left(x + 15\right)}^{2} + {\left(y - 12\right)}^{2} = 25$ is of the form ${\left(x - p\right)}^{2} + {\left(y - q\right)}^{2} = {r}^{2}$, which is a circle. The radius, $r$ will stretch to the circumference on all sides of the centre, so it will determine how far you can step without losing contact with the motion detector.

Here, ${r}^{2} = 25$, so $r = 5$ (the radius must be positive).

Therefore, you can step $5$ feet in any direction and be detected.

Hopefully this helps!