Question

give the center and radius of the circle. $(x - 5)^{2}+y^{2}=16$ center: radius:

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: Identify the center

For the equation \((x - 5)^{2}+y^{2}=16\), comparing with \((x - h)^{2}+(y - k)^{2}=r^{2}\), we have \(h = 5\) and \(k=0\). So the center is \((5,0)\).

Step3: Identify the radius

Since \(r^{2}=16\), then \(r=\sqrt{16}=4\) (we take the positive value as radius is non - negative).

Answer:

Center: \((5,0)\)
Radius: \(4\)