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. $(x + 3)^{2}+(y + 5)^{2}=4$ the center is $(-3,-5)$. (type an ordered pair. simplify your answer.) the radius is $square$. (type an integer or a simplified fraction.)

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: Compare the given equation with the standard form

Given \((x + 3)^2+(y + 5)^2 = 4\), we can rewrite it as \((x-(-3))^2+(y-(-5))^2=2^2\).

Answer:

The radius is \(2\).