Question

find the center and the radius of the circle. then graph the circle.
( x^2 + y^2 = 16 )
the center is (square).
(type an ordered pair. type an integer or a fraction.)

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 given equation

The given equation is \(x^2 + y^2 = 16\), which can be rewritten as \((x - 0)^2 + (y - 0)^2 = 4^2\). By comparing with the standard form, we see that \(h = 0\), \(k = 0\), and \(r = 4\).

Answer:

The center is \((0, 0)\).