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It looks like you've uploaded an image containing problems related to writing the standard form equation of circles. I see you mentioned a specific example with a center at (12, -10) and a radius of 3. 

Let's work through the general form for this specific circle.

### Equation of a Circle

The standard form of the equation of a circle is given by:

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

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

### Given:
- Center: \((12, -10)\)
- Radius: \(3\)

### Substituting into the formula:

\[
(x - 12)^2 + (y + 10)^2 = 3^2
\]

Simplifying the radius:

\[
(x - 12)^2 + (y + 10)^2 = 9
\]

This is the standard form equation for the circle.

Would you like further details on any part of this, or help with any of the other problems on the worksheet?

Here are 8 follow-up questions to expand on this information:
1. How would you expand the standard form to convert it to general form?
2. What would the equation look like if the radius was doubled?
3. How would the equation change if the circle was centered at the origin?
4. How can you determine the center and radius directly from a standard form equation?
5. What is the distance from the origin to the center of this circle?
6. How do you find the intersection points of this circle with the x-axis?
7. How do you find the intersection points of this circle with the y-axis?
8. How does the equation of a circle change if it is translated horizontally or vertically?

**Tip:** When working with circle equations, always double-check your signs for the center coordinates to avoid common mistakes!

Learn how to write the standard form equation of a circle given its center at (12, -10) and a radius of 3. This problem involves key geometric concepts and the application of the standard form formula for circles. Suitable for high school students.

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