Question

$x^{2}+y^{2}=16$ a. b. c.

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. For the equation \(x^2 + y^2 = 16\), we can rewrite it as \((x - 0)^2 + (y - 0)^2 = 4^2\). So the center is \((0, 0)\) and the radius is \(4\).

Step2: Analyze each graph

• Option A: The center of the circle is not at \((0, 0)\), so this is incorrect.
• Option B: The center of the circle is not at \((0, 0)\), so this is incorrect.
• Option C: The center of the circle is at \((0, 0)\) (on the y - axis, at the origin's vertical line) and the radius seems to be \(4\) (since it extends from, say, \(y=- 4\) to \(y = 4\) or \(x=-4\) to \(x = 4\) approximately), which matches the equation \(x^{2}+y^{2}=16\) (center \((0,0)\), radius \(4\)).

Answer:

C. The graph with center at \((0,0)\) (on the y - axis) and radius \(4\)