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.
$(x + 4)^{2}+(y + 3)^{2}=4$
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's equation

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 \((x + 4)^2+(y + 3)^2 = 4\), we can rewrite it as \((x-(-4))^2+(y-(-3))^2=2^2\). So, \(h=-4\) and \(k = - 3\). The center \((h,k)\) is \((-4,-3)\).

Step3: Identify the radius

Since \(r^2 = 4\), then \(r=\sqrt{4}=2\).

Answer:

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