Question

determine the center and radius of the circle $x^{2}+y^{2}=16$. enter the center as a point $(a,b)$. the center is . the radius is .

Explanation:

Step1: Recall circle - standard 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.
The given equation $x^{2}+y^{2}=16$ can be written as $(x - 0)^2+(y - 0)^2 = 4^2$.

Step2: Determine the center

Comparing with the standard - form, when $a = 0$ and $b = 0$, the center of the circle is $(0,0)$.

Step3: Determine the radius

Since $r^{2}=16$, taking the square root of both sides (and considering $r>0$), we get $r = 4$.

Answer:

The center is $(0,0)$.
The radius is $4$.