Write in standard form: center at (15, -20), radius = 9

The equation of a circle in standard form is:

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

Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius.

Given:
- Center \((h, k) = (15, -20)\)
- Radius \(r = 9\)

Substituting these values into the standard form:

\[
(x - 15)^2 + (y + 20)^2 = 9^2
\]

Simplifying:

\[
(x - 15)^2 + (y + 20)^2 = 81
\]

So, the equation of the circle in standard form is:

\[
(x - 15)^2 + (y + 20)^2 = 81
\]

Would you like further details on any part of this process or have any questions?

Here are some related questions you might be interested in:
1. How do you find the equation of a circle given two points on the circumference?
2. What is the general form of a circle's equation, and how does it differ from the standard form?
3. How do you find the center and radius from the general form of a circle's equation?
4. How can you convert the equation of a circle from standard form to general form?
5. What is the distance formula, and how does it relate to the radius of a circle?
6. How do you find the equation of a circle given the endpoints of a diameter?
7. What are the steps to complete the square when deriving the standard form of a circle?
8. How do you graph a circle given its standard form equation?

**Tip:** Always double-check your signs when substituting values into the standard form equation, especially when dealing with negative coordinates.

Learn how to derive the equation of a circle with center at (15, -20) and radius 9. This problem involves applying the standard form of a circle's equation, focusing on mathematical concepts in geometry. Suitable for high school students.

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