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.
$\square$ (type an integer or a decimal.)

Explanation:

Step1: Recall the standard circle equation

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 \(r^2\) from the given equation

In the equation \((x - 4)^2 + (y - 5)^2 = 64\), we have \(r^2 = 64\).

Step3: Solve for \(r\)

To find \(r\), take the square root of both sides: \(r=\sqrt{64}\). Since the radius is a non - negative quantity, \(r = 8\).

Answer:

8