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The problem is asking for the equation of a circle with its center at the origin and passing through the point \((-9, 0)\).

### Equation of a Circle:
The standard equation of a circle with center at the origin \((0, 0)\) and radius \(r\) is:

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

### Finding the Radius:
To find the radius, we use the distance formula between the center \((0, 0)\) and the given point \((-9, 0)\). The distance formula is:

\[
r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the values:

\[
r = \sqrt{(-9 - 0)^2 + (0 - 0)^2} = \sqrt{(-9)^2} = 9
\]

So the radius \(r\) is 9.

### Equation of the Circle:
Now that we know the radius, the equation of the circle becomes:

\[
x^2 + y^2 = 9^2
\]

Simplifying:

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

Thus, the equation of the circle is:

\[
\boxed{x^2 + y^2 = 81}
\]

Let me know if you need further details or have questions!

Here are 5 related questions to consider:
1. How do you find the equation of a circle if the center is not at the origin?
2. What is the general form of a circle's equation with a center at \((h, k)\)?
3. How can you find the radius if you are given two points on the circumference?
4. What would the equation look like if the point was at \((0, -9)\)?
5. How do you graph a circle using its equation?

**Tip:** For any circle, the distance from the center to any point on the circle is always the radius. This is a key property to use in solving circle-related problems.

Dar la ecuación del círculo con centro en el origen y que atraviesa el punto (-9, 0).

Learn how to find the equation of a circle with its center at the origin (0, 0) and passing through the point (-9, 0). This example uses the standard equation of a circle and basic distance formula, suitable for Grades 9-10 students.

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