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.
$x^{2}+y^{2}-2x - 6y - 26 = 0$
the equation in standard form is $(x - 1)^{2}+(y - 3)^{2}=36$
(simplify your answer.)
the center of the circle is
(type an ordered pair.)

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: Identify \(h\) and \(k\) from the given standard - form equation \((x - 1)^2+(y - 3)^2=36\)

Comparing \((x - 1)^2+(y - 3)^2=36\) with \((x - h)^2+(y - k)^2=r^2\), we can see that \(h = 1\) and \(k=3\).

Answer:

The center of the circle is \((1,3)\)