https://file.aiquickdraw.com/mathbot/file/1726370964996fjy15ca1.jpg

The problem asks to graph a circle with the given center \((h, k) = (0, 0)\) and radius \(r = 9\).

The equation of a circle is given by:

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Since the center is \((0, 0)\), and the radius is 9, the equation becomes:

\[
x^2 + y^2 = 81
\]

This means that the circle is centered at the origin and has a radius of 9 units.

Looking at the images provided:
- The correct graph should have a circle centered at \((0, 0)\) and passing through points that are 9 units away from the center (like \((9, 0)\), \((0, 9)\), \((-9, 0)\), and \((0, -9)\)).

The correct graph is the **first option** since it shows a circle centered at the origin with a radius of 9 units.

Would you like more details or have any other questions?

Here are five related questions for deeper understanding:
1. What is the general formula for the equation of a circle?
2. How do you find the radius of a circle from its equation?
3. How would the graph change if the center were moved to \((3, 4)\)?
4. What is the effect on the graph of a circle if the radius is doubled?
5. How can you graph a circle if given only its equation?

**Tip**: When graphing circles, always check the center and radius in the equation to make sure they are correctly represented on the graph.

Graph the circle whose radius is r and whose center is (h, k). Given: r = 9; (h, k) = (0, 0).

Learn how to graph a circle with a center at the origin (0, 0) and a radius of 9 units. Understand the equation of a circle and identify the correct graph representation. Suitable for students in Grades 9-10.

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