Question

give the center and radius of the circle described by the equation and graph the and range.

(x - 1)^2 + (y - 2)^2 = 49

what is the center of the circle?

the circle is centered at the point (1,2).

(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 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 \((x - 1)^2+(y - 2)^2 = 49\), we can rewrite \(49\) as \(7^2\).
Since \(r^2=49\), then \(r=\sqrt{49}\).

Answer:

The radius of the circle is \(7\).