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 $square$

(type an integer or a fraction.)

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: Compare with the given equation

The given equation is \(x^{2}+(y - 1)^{2}=16\), which can be written as \((x-0)^2+(y - 1)^2 = 4^2\).

Answer:

The radius of the circle is \(4\).