Question

find the center and radius of the circle (x - 1)^2 + (y + 2)^2 = 36

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 \((x - 1)^2+(y+2)^2 = 36\), comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 1\) and \(k=-2\). So the center \((h,k)=(1,-2)\).

Step3: Identify the radius

Since \(r^2 = 36\), then \(r=\sqrt{36}=6\).

Answer:

The center of the circle is \((1,-2)\) and the radius is \(6\).