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 $(-4,3)$.
(type an ordered pair. simplify your answer.)
the radius is $5$.
(type an integer or a simplified fraction.)
graph the circle.

express the domain of the relation in interval notation.

Explanation:

Step1: Recall the domain formula for a circle

The domain of a circle \((x - h)^2+(y - k)^2=r^2\) is given by \(h - r\leqslant x\leqslant h + r\).
Here, \(h=-4\) and \(r = 5\).

Step2: Calculate the lower and upper bounds of the domain

For the lower - bound: \(x=h - r=-4-5=-9\).
For the upper - bound: \(x=h + r=-4 + 5=1\).

Answer:

\([-9,1]\)