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.
$(x + 4)^2 + (y - 3)^2 = 25$
the center is \\(\square\\).
(type an ordered pair. simplify your answer.)

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: Rewrite the given equation to match the standard form

Given \((x + 4)^2+(y - 3)^2=25\), we can rewrite \((x + 4)\) as \((x-(- 4))\). So the equation becomes \((x-(-4))^2+(y - 3)^2=5^2\).

Answer:

\((-4,3)\)