Question

give the center and radius of the circle described by the equation and graph the equation. use the graph to identify the relations domain and range.

$x^{2}+(y - 1)^{2}=16$

what is the center of the circle?

the circle is centered at the point $(0,1)$

(type an ordered pair.)

what is the radius of the circle?

the radius of the circle is 4

(type an integer or a fraction.)

use the graphing tool to graph the circle.

what is the domain?

the domain is $(0,1)$

(type your answer in interval notation.)

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.
For the given equation \(x^{2}+(y - 1)^{2}=16\), we can rewrite it as \((x-0)^2+(y - 1)^2 = 4^2\).

Step2: Find the domain

The domain of a circle \((x - h)^2+(y - k)^2=r^2\) is given by \(h - r\leqslant x\leqslant h + r\).
Here, \(h = 0\) and \(r = 4\), so \(0-4\leqslant x\leqslant0 + 4\), which is \([-4,4]\).

Answer:

The domain is \([-4,4]\)