Problem

Identify the center and radius of the circle given by the equation \((x - 3)^2 + (y + 2)^2 = 25\).

Answer

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Answer

Taking the square root of \(r^2\) will give us the radius \(r\).

Steps

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 \(r\).

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