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 $(-2,3)$.
(type an ordered pair. simplify your answer.)
the radius is
(type an integer or a simplified fraction.)

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 in the standard form

The given equation is \((x + 2)^2+(y - 3)^2=16\), which can be written as \((x-(- 2))^2+(y - 3)^2 = 4^2\).

Answer:

The radius is \(4\)