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 rang
$(x + 5)^{2}+(y - 1)^{2}=25$
the center is $(-5,1)$.
(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 \((x + 5)^2+(y - 1)^2=25\), we can rewrite \((x + 5)^2\) as \((x-(- 5))^2\) and \(25\) as \(5^2\).
So, \(h=-5\), \(k = 1\), and \(r^2 = 25\).

Step3: Find the radius

Since \(r^2=25\), taking the square root of both sides (and considering \(r\geq0\) for the radius of a circle), we get \(r=\sqrt{25}=5\).

Answer:

The radius is \(5\)