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.
$(x + 4)^2 + (y - 3)^2 = 25$
the center is $(-4,3)$.
(type an ordered pair. simplify your answer.)
the radius is \boxed{}.
(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 \((x + 4)^2+(y - 3)^2=25\), we can rewrite \((x + 4)\) as \((x-(-4))\) and \(25\) as \(5^2\). So, \(h=-4\), \(k = 3\), and \(r^2=25\).

Step3: Solve for the radius

Since \(r^2 = 25\), taking the square root of both sides gives \(r=\sqrt{25}=5\).

Answer:

\(5\)