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.
$(x + 2)^{2}+(y + 6)^{2}=25$
the center is $(-2,-6)$.
(type an ordered pair. simplify your answer.)
the radius is
(type an integer or a simplified fraction.)

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: Compare the given equation with the standard form

Given \((x + 2)^2+(y + 6)^2 = 25\), we can rewrite it as \((x-(-2))^2+(y-(-6))^2=5^2\).

Answer:

The radius is \(5\)