Question

the equation of a circle is given below. identify the center and radius. then graph the circle.

$x^{2}+y^{2}=16$

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: Rewrite the given equation in standard form

The given equation \(x^{2}+y^{2}=16\) can be rewritten as \((x - 0)^2+(y - 0)^2 = 4^2\).

Answer:

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