This circle is centered at the origin, and the length of its radius is 2. What is the circle's equation?

1. Break Down the Problem

We need to find the equation of a circle that is centered at the origin $(0, 0)$ with a radius of $2$.

2. Relevant Concepts

The standard form of the equation of a circle centered at the origin is given by: $x^2 + y^2 = r^2$ where $r$ is the radius of the circle.

3. Analysis and Detail

Given the radius $r = 2$, we can substitute this value into the standard equation: $x^2 + y^2 = 2^2$

4. Verify and Summarize

Calculating $2^2$ gives us $4$. Thus, the verified equation of the circle becomes: $x^2 + y^2 = 4$

Final Answer

The equation of the circle is: $x^2 + y^2 = 4$