Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.

the center is

(type an ordered pair. simplify your answer.)

the radius is

(type an integer or a simplified fraction.)

graph the circle.

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 and \(r\) is the radius.

Step2: Identify the center

For the equation \((x + 4)^{2}+(y + 3)^{2}=4\), we can rewrite it as \((x-(-4))^{2}+(y-(-3))^{2}=2^{2}\). Comparing with the standard form \((x - h)^{2}+(y - k)^{2}=r^{2}\), we get \(h=-4\) and \(k = - 3\). So the center \((h,k)=(-4,-3)\).

Step3: Identify the radius

Since the equation is \((x + 4)^{2}+(y + 3)^{2}=4\), and \(4 = 2^{2}\). Comparing with the standard form \((x - h)^{2}+(y - k)^{2}=r^{2}\), we get \(r = 2\).

Answer:

The center is \((-4,-3)\) and the radius is \(2\).