Question

give the center and radius of the circle. $(x + 1)^{2}+(y - 1)^{2}=4$ center: radius:

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: Rewrite the given equation to match the standard form

The given equation \((x + 1)^2+(y - 1)^2 = 4\) can be rewritten as \((x-(-1))^2+(y - 1)^2=2^2\).

Step3: Identify the center \((h,k)\)

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

Step4: Identify the radius \(r\)

Since \(r^2 = 4\), then \(r=\sqrt{4}=2\).

Answer:

Center: \((-1,1)\)
Radius: \(2\)