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.
(type an ordered pair.)

Explanation:

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 \(k = 5\).

Answer:

\((4, 5)\)