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.
$(x + 3)^{2}+(y - 1)^{2}=9$
the center is $(-3,1)$
(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 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 with the given equation

Given \((x + 3)^2+(y - 1)^2=9\), we can rewrite \((x+3)\) as \((x-(- 3))\) and \(9\) as \(3^2\). So, comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=-3\), \(k = 1\), and \(r^2=9\).

Step3: Solve for the radius

Since \(r^2 = 9\), taking the square root of both sides (and considering \(r>0\) for the radius of a circle), we get \(r=\sqrt{9}=3\).

Answer:

\(3\)