Question

determine the center and radius of the circle. write your answers in simplified exact form.

$x^{2}+y^{2}=20$

part 1 of 2

the center is $(0,0)$.

part: $1 / 2$

part 2 of 2

the radius is $r=$

Explanation:

Step1: Recall the standard form of a circle's 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.

Step2: Rewrite the given equation in standard form

The given equation \(x^{2}+y^{2}=20\) can be written as \((x - 0)^2+(y - 0)^2=(\sqrt{20})^2\).

Step3: Simplify \(\sqrt{20}\)

We know that \(\sqrt{20}=\sqrt{4\times5}=\sqrt{4}\times\sqrt{5}=2\sqrt{5}\).

Answer:

The radius is \(r = 2\sqrt{5}\)