https://file.aiquickdraw.com/mathbot/file/1726449788310ud5oaav1.jpg

The equation of the circle drawn above is :

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.

The equation of the circle drawn above is:

Learn how to find the equation of a circle centered at the origin with a radius of 6 units. The solution covers essential concepts in coordinate geometry and the standard equation of a circle, ideal for students in Grades 9-12.

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