Question

the equation of a circle centered at the origin is $x^{2}+y^{2}=16$. what is the radius of the circle?
a. 256
b. 4
c. 16
d. 8

Explanation:

Step1: Recall circle - equation formula

The standard equation of a circle centered at the origin \((0,0)\) is \(x^{2}+y^{2}=r^{2}\), where \(r\) is the radius.

Step2: Compare given equation with standard form

Given \(x^{2}+y^{2}=16\), and since \(x^{2}+y^{2}=r^{2}\), then \(r^{2}=16\).

Step3: Solve for \(r\)

Take the square - root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = \sqrt{16}=4\).

Answer:

B. 4