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.
$(x - 3)^{2}+(y - 6)^{2}=4$
what is the radius of the circle?
the radius of the circle is 2.
(type an integer or a fraction.)
use the graphing tool to graph the circle.

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

Given \((x - 3)^2+(y - 6)^2 = 4\), we can rewrite \(4\) as \(2^2\). So, \(r^2=2^2\).

Step3: Find the radius

Taking the square root of both sides (since radius \(r>0\)), we get \(r = 2\).

Answer:

The radius of the circle is \(2\).