Question

identify the center and the radius for $(x + 2)^{2}+(y - 1)^{2}=9$.
the center would be ().
(enter answer in (x,y) form)
the radius would be.
use / to indicate a fraction...for example $\frac{1}{2}$ would be entered as 1/2
an improper fraction should be entered as a mixed number...for example $\frac{15}{2}$ would be entered as 7 1/2

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: Identify the center

For the equation \((x + 2)^2+(y - 1)^2 = 9\), rewrite \(x+2\) as \(x-(-2)\). Comparing with \((x - h)^2+(y - k)^2 = r^2\), we have \(h=-2\) and \(k = 1\). So the center is \((-2,1)\).

Step3: Identify the radius

Since \(r^2=9\), then \(r=\sqrt{9}=3\).

Answer:

The center is \((-2,1)\) and the radius is \(3\).