Question

the equation of a circle is given below. identify the radius and center. then graph the circle. (x + 4)^2+(y - 2)^2 = 16

Explanation:

Step1: Recall circle - equation form

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

Step2: Identify the center

For the equation $(x + 4)^2+(y - 2)^2=16$, we have $x+4=x-(-4)$ and $y - 2$ as is. So, $h=-4$ and $k = 2$, and the center is $(-4,2)$.

Step3: Identify the radius

Since $r^2 = 16$, taking the square - root of both sides (and considering the non - negative value for radius), we get $r=\sqrt{16}=4$.

Answer:

Radius: 4
Center: $(-4,2)$