Question

multiple choice 10 points a circle has the equation $x^2 + y^2 = 16$. what is the radius of the circle? 8 16 4 32 256

Explanation:

Step1: Recall circle equation form

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 given equation \(x^2 + y^2 = 16\), we can rewrite it as \(x^2 + y^2 = 4^2\) (since \(16 = 4\times4\)).

Step2: Identify radius from equation

Comparing with the standard form \((x - 0)^2 + (y - 0)^2 = r^2\) (here \(h = 0\), \(k = 0\), so the center is at the origin), we see that \(r^2 = 16\), so taking the square root of both sides (and since radius is positive), \(r=\sqrt{16}=4\).

Answer:

4 (corresponding to the option with "4" as the text, e.g., if the option is labeled as, say, C. 4, then the answer would be C. 4)