To find the equation of the circle in the given graph, we need to determine two things:

1. The center of the circle $(h, k)$
2. The radius $r$

From the image:

• The center of the circle appears to be at the origin $(0, 0)$.
• The radius can be determined by counting the number of grid units from the center to the boundary of the circle. It looks like the radius is 6 units (from $(0,0)$ to $(6, 0)$, $(0, 6)$, etc.).

Standard equation of a circle:

$(x - h)^2 + (y - k)^2 = r^2$ Where $(h, k)$ is the center and $r$ is the radius.

Since the center is $(0, 0)$ and the radius is 6, the equation becomes: $x^2 + y^2 = 6^2$ $x^2 + y^2 = 36$

Thus, the equation of the circle is: $x^2 + y^2 = 36$

Would you like further explanation or details?

Here are some related questions to consider:

1. What is the general form of the equation of a circle with a different center?
2. How can we determine the equation of a circle given any two points on its circumference?
3. What is the equation of a circle if its radius is doubled?
4. How can this equation be derived if the center is shifted to $(2, 3)$?
5. How can you find the distance between a point and the center of the circle?

Tip: When working with equations of circles, always identify the center and radius first, as they directly define the equation.