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To convert the given equation from standard form to general form, we need to expand the squared terms and simplify.

### Given Equation:
\[
(x - 1)^2 + (y + 9)^2 = 28
\]

### Steps to Convert:

1. **Expand the squared terms**:
   \[
   (x - 1)^2 = x^2 - 2x + 1
   \]
   \[
   (y + 9)^2 = y^2 + 18y + 81
   \]

2. **Substitute these into the original equation**:
   \[
   x^2 - 2x + 1 + y^2 + 18y + 81 = 28
   \]

3. **Combine like terms**:
   \[
   x^2 + y^2 - 2x + 18y + 82 = 28
   \]

4. **Move the constant to the left side to set the equation equal to 0**:
   \[
   x^2 + y^2 - 2x + 18y + 54 = 0
   \]
   (where \( 82 - 28 = 54 \))

### General Form:
\[
x^2 + y^2 - 2x + 18y + 54 = 0
\]

This is the general form of the equation of the circle.

Would you like more details or have any questions about this process?

### Related Questions:
1. How do you expand binomials involving squared terms?
2. What is the significance of converting between standard and general forms of a circle's equation?
3. How do you determine the center and radius of a circle from the general form?
4. Can this process be applied to ellipses or hyperbolas?
5. What are the differences between standard form and general form equations for conic sections?

### Tip:
When converting from standard to general form, carefully expand and combine like terms to avoid mistakes in simplifying the equation.

Learn how to convert a circle's equation from standard to general form using algebraic methods. This guide covers expanding squared terms, combining like terms, and deriving the general form equation. Suitable for high school students and anyone interested in circle equations.

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