Problem
Identify the center and radius of the circle given by the equation \((x - 3)^2 + (y + 2)^2 = 25\).
Solution
Step 1 ：The general form of a circle equation is \((x - a)^2 + (y - b)^2 = r^2\) where \((a, b)\) is the center of the circle and \(r\) is the radius.
Step 2 ：Comparing this with our given equation, we can see that \(a = 3\), \(b = -2\), and \(r^2 = 25\).
Step 3 ：Taking the square root of \(r^2\) will give us the radius \(r\).
