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.
$(x + 2)^{2}+(y - 3)^{2}=16$
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 \((x + 2)^2+(y - 3)^2=16\), we can rewrite \((x + 2)\) as \((x-(- 2))\). So, comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h=-2\), \(k = 3\).

Answer:

\((-2,3)\)