Question

give the center and radius of the circle. $x^{2}+(y - 4)^{2}=9$ center: radius:

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: Identify the center

For the equation \(x^{2}+(y - 4)^{2}=9\), compare with \((x - h)^2+(y - k)^2=r^2\). Here \(h = 0\) (since \(x=x-0\)) and \(k = 4\). So the center is \((0,4)\).

Step3: Identify the radius

Since \(r^{2}=9\), then \(r=\sqrt{9}=3\) (radius is non - negative).

Answer:

Center: \((0,4)\)
Radius: \(3\)