The problem asks for the equation of a circle centered at the origin $(0, 0)$ with a radius of 12.

1. Problem Description

The problem asks for the equation of a circle centered at the origin $(0, 0)$ with a radius of

1

2.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is given by:

$(x - h)^2 + (y - k)^2 = r^2$

In this case, the center is at the origin $(0, 0)$, so $h = 0$ and $k = 0$. The radius is $r = 12$. Substituting these values into the general equation, we get:

$(x - 0)^2 + (y - 0)^2 = 12^2$

Simplifying this equation gives:

$x^2 + y^2 = 144$

3. Final Answer

$x^2 + y^2 = 144$