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To find the equation of a circle centered at the origin \((0, 0)\) and passing through the point \((0, 10)\), we can use the standard form of a circle equation:

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

Since the circle passes through \((0, 10)\), the radius \(r\) is the distance from the origin to this point, which is \(10\).

Thus, the equation of the circle is:

\[
x^2 + y^2 = 10^2
\]

Simplifying, we get:

\[
x^2 + y^2 = 100
\]

Would you like a detailed explanation? Here are some related questions:

1. What is the general equation for a circle centered at any point \((h, k)\)?
2. How do you find the radius of a circle when given two points on its diameter?
3. What if the circle passed through a different point, like \((5, 5)\)?
4. Can this method be used for circles not centered at the origin?
5. How do you graph a circle equation?

**Tip:** Always check if the point given is on the circle by substituting it into the equation.

Give the equation of the circle centered at the origin and passing through the point (0, 10).

Learn how to find the equation of a circle centered at the origin that passes through a given point, specifically (0, 10). This problem uses the standard circle equation x^2 + y^2 = r^2 and explores basic geometric concepts. Suitable for students in Grades 9-10.

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