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.

click to enlarge graph

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 center

For the equation \(x^{2}+(y - 1)^{2}=16\), we can rewrite it as \((x-0)^2+(y - 1)^2 = 4^2\). Comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 0\) and \(k=1\). So the center \((h,k)=(0,1)\).

Step3: Identify the radius

Since the equation is \((x-0)^2+(y - 1)^2 = 4^2\), comparing with \((x - h)^2+(y - k)^2=r^2\), we get \(r = 4\).

Answer:

The center of the circle is \((0,1)\) and the radius is \(4\).