Question

find the center and the radius of the circle. then graph the circle. ( x^2 + y^2 = 16 ) the center is (0,0). (type an ordered pair. type an integer or a fraction) the radius is 4. (type an integer or a fraction.) use the graphing tool on the right to graph the circle. click to enlarge graph

Explanation:

Step1: Recall the standard circle 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

The given equation is \(x^2 + y^2 = 16\). We can rewrite it as \((x - 0)^2 + (y - 0)^2 = 4^2\).

Step3: Identify center and radius

By comparing with the standard form, we see that \(h = 0\), \(k = 0\), so the center is \((0, 0)\). And \(r^2 = 16\), so taking the square root (since radius is positive), \(r = \sqrt{16} = 4\).

Answer:

The center is \((0, 0)\) and the radius is \(4\).