Question

(x - 5)^2 + (y - 4)^2 = 36

Explanation:

Step1: Recall the circle equation formula

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: Identify \(h\), \(k\), and \(r\) from the given equation

For the equation \((x - 5)^2 + (y - 4)^2 = 36\), we compare it with the standard form. Here, \(h = 5\), \(k = 4\), and \(r^2 = 36\), so \(r=\sqrt{36}=6\).

Answer:

The center of the circle is \((5, 4)\) and the radius is \(6\).