Question

what is the diameter of the circle $x^{2}+y^{2}=16$? write your answer in simplified, rationalized form.

Explanation:

Step1: Recall circle - equation form

The standard form of a circle equation is $(x - a)^2+(y - b)^2=r^2$, where $(a,b)$ is the center and $r$ is the radius. For the equation $x^{2}+y^{2}=16$, it can be written as $(x - 0)^2+(y - 0)^2 = 4^2$, so the radius $r = 4$.

Step2: Calculate the diameter

The diameter $d$ of a circle is related to the radius by the formula $d = 2r$. Substituting $r = 4$ into the formula, we get $d=2\times4$.

Answer:

8