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.
$(x + 5)^{2}+(y - 1)^{2}=25$
the center is .
(type an ordered pair. simplify your answer.)

Explanation:

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

Given \((x + 5)^{2}+(y - 1)^{2}=25\), we can rewrite \(x+5\) as \(x-(-5)\). So the equation becomes \((x - (-5))^{2}+(y - 1)^{2}=5^{2}\).

Answer:

The center is \((-5,1)\)