Question

give the center and radius of the circle described by the equation and and range. ((x - 5)^2+(y - 5)^2 = 4) what is the center of the circle? the circle is centered at the point ((5,5)) (type an ordered pair.) what is the radius of the circle? the radius of the circle is 2 (type an integer or a fraction.) use the graphing tool to graph the circle

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 \((x - 5)^2+(y - 5)^2 = 4\), comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 5\) and \(k = 5\). So the center is \((5,5)\).

Step3: Identify the radius

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

Answer:

The center of the circle is \((5,5)\) and the radius is \(2\).