Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the domain and range.
$(x + 6)^{2}+(y - 1)^{2}=36$
the center is
(type an ordered pair. simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's 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: Rewrite the given equation to match the standard form

Given \((x + 6)^2+(y - 1)^2=36\), we can rewrite \((x+6)\) as \((x-(-6))\). So the equation becomes \((x-(-6))^2+(y - 1)^2=6^2\).

Answer:

The center is \((-6,1)\)