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.
$(x + 3)^2+(y + 5)^2 = 4$
the center is $(-3,-5)$.
(type an ordered pair. simplify your answer.)
the radius is $2$.
(type an integer or a simplified fraction.)
graph the circle.
express the domain of the relation in interval notation.

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: Identify the domain

For the circle \((x + 3)^2+(y + 5)^2=4\) (or \((x-(-3))^2+(y-(-5))^2 = 2^2\)), the \(x\) - values range from \(h - r\) to \(h + r\). Here \(h=-3\) and \(r = 2\). So \(x\) ranges from \(-3-2=-5\) to \(-3 + 2=-1\).

Answer:

\([-5,-1]\)