Question

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

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

Step3: Identify the radius

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

Answer:

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