Question

sketch the graph of the equation. if the graph is a parabola, find its vertex. if the graph is a circle, find its center and radius.
$x^2 + y^2 = 16$
use the graphing tool to graph the equation.
select the correct choice below and fill in the answer box(es) to complete your choice.
a. the graph is a parabola with the vertex located at. (type an ordered pair.)
b. the graph is a circle with radius. (simplify your answer. type an exact answer, using radicals as needed.)
the center is located at. (type an ordered pair.)

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2 = r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Compare the given equation with the standard form

The given equation is \(x^{2}+y^{2}=16\). We can rewrite it as \((x - 0)^{2}+(y - 0)^{2}=4^{2}\). By comparing with the standard form \((x - h)^2+(y - k)^2=r^2\), we can see that \(h = 0\), \(k = 0\) and \(r = 4\). So the graph is a circle with center \((0,0)\) and radius \(4\).

Answer:

B. The graph is a circle with radius \(4\). The center is located at \((0,0)\)