Question

give the center and radius of the circle described by 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'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 the given equation with the standard form

Given \((x - 1)^2+(y - 2)^2 = 49\). We can rewrite \(49\) as \(7^2\). So, comparing with \((x - h)^2+(y - k)^2=r^2\), we have \(h = 1\), \(k=2\), and \(r^2=49\).

Step3: Solve for the radius \(r\)

If \(r^2 = 49\), then taking the square root of both sides (since \(r>0\) for the radius of a circle), \(r=\sqrt{49}=7\).

Answer:

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