Question

complete the square and write the given equation in standard form. then give the center and radius of the circle and graph the equation.

x² + y² - 4x - 6y - 23 = 0

the equation in standard form is (x - 2)² + (y - 3)² = 36. (simplify your answer.)

the center of the circle is (2,3). (type an ordered pair.)

the radius of the circle is r =

Explanation:

Step1: Recall the standard form of a circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Extract \(r\) from the given standard form

Given \((x - 2)^2+(y - 3)^2 = 36\), and since \(r^2=36\).
Take the square root of both sides: \(r=\sqrt{36}\)

Answer:

\(6\)