Question

a circular walking path is modeled by (x - 3)^2 + (y + 8)^2 = 36, where all measurements are in meters. what are the center and radius of the path?
center at (-3, 8); r = 6
center at (-3, 8); r = 36
center at (3, -8); r = 6
center at (3, 8); r = 36

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle 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 center

For the equation $(x - 3)^2+(y + 8)^2 = 36$, comparing with the standard form, we have $h = 3$ and $k=-8$. So the center of the circle is $(3,-8)$.

Step3: Identify the radius

Since $r^2=36$, taking the square - root of both sides (and considering the non - negative value for the radius), we get $r = 6$.

Answer:

C. Center at $(3, -8); r = 6$