Question

find the center and the radius of the circle.
$(x - 9)^2 + (y + 2)^2 = 39$
the center is $(9, -2)$
(type an ordered pair.)
the radius is $square$
(type an exact answer, using radicals as needed.)

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 \(r^2\) from given equation

Given \((x - 9)^2 + (y + 2)^2 = 39\), we compare with the standard form. Here, \(r^2 = 39\).

Step3: Solve for \(r\)

To find \(r\), take the square root of both sides: \(r = \sqrt{39}\) (since radius is positive).

Answer:

\(\sqrt{39}\)