The equation of a circle is given below. Identify the center and the radius. Then graph the \[ x^{2}+4 y+y^{2}-12=0 \]

Step 1 ：The given equation is not in 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 of the circle and \(r\) is the radius.

Step 2 ：To identify the center and the radius of the circle, we need to rewrite the given equation in the standard form.

Step 3 ：The given equation can be rewritten as \((x-0)^2 + (y+2)^2 = 4^2\).

Step 4 ：From this, we can see that the center of the circle is at \((0, -2)\) and the radius is \(4\).

Step 5 ：\(\boxed{\text{Final Answer: The center of the circle is at }(0, -2)\text{ and the radius is }4\}