Question

sketch the graph of the following circle. ((x - 4)^2 + (y - 5)^2 = 64) (a) find the center of the circle. (b) find the radius of the circle. (c) graph the circle. (a) find the center of the circle. ((4,5)) (type an ordered pair.) (b) find the radius of the circle. (8) (type an integer or a decimal.) (c) graph the circle. use the graphing tool to graph the circle. click to enlarge graph

Explanation:

Part (a)

Step1: Recall circle equation form

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 \(h\) and \(k\)

For the equation \((x - 4)^2 + (y - 5)^2 = 64\), compare with the standard form. Here, \(h = 4\) and \(k = 5\). So the center is \((4, 5)\).

Step1: Recall radius from equation

From the standard form \((x - h)^2 + (y - k)^2 = r^2\), \(r^2 = 64\).

Step2: Solve for \(r\)

Take the square root of both sides: \(r=\sqrt{64}=8\).

Answer:

\((4, 5)\)

Part (b)