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.

$(x - 5)^2+(y - 6)^2 = 4$

what is the center of the circle?

the circle is centered at the point $(5,6)$

(type an ordered pair.)

what is the radius of the circle?

the radius of the circle is

(type an integer or a fraction.)

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: Compare with the given equation

Given \((x - 5)^{2}+(y - 6)^{2}=4\), we can rewrite \(4\) as \(2^{2}\).
So, \(r^{2}=2^{2}\).

Answer:

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