To determine the equation of the circle in the graph, let's examine its center and radius.

1. Center: From the graph, the circle is centered at the origin $(0, 0)$.

2. Radius: The radius can be observed by measuring the distance from the center to any point on the circle. From the origin, the circle extends up to $y = 6$, so the radius is $6$.

Using the standard form of a circle's equation, $(x - h)^2 + (y - k)^2 = r^2$, where $(h, k)$ is the center and $r$ is the radius, we get:

$(x - 0)^2 + (y - 0)^2 = 6^2$

This simplifies to:

$x^2 + y^2 = 36$

The equation of the circle is:

$x^2 + y^2 = 36$

Would you like more details on this solution or have further questions?

1. How do we determine the center of a circle from its graph?
2. What is the general formula for the equation of a circle?
3. How can the radius be derived from a given circle equation?
4. What if the circle's center was not at the origin?
5. How can transformations affect the equation of a circle?

Tip: The radius is always the square root of the constant on the right side of the circle equation.