https://file.aiquickdraw.com/mathbot/file/1726711710441cl03fqcf.jpg

The given equation is:

\[
(x - 11)^2 + (y + 13)^2 = 25
\]

This represents the equation of a circle in standard form, where the center is \((h, k) = (11, -13)\), and the radius is \(\sqrt{25} = 5\).

To convert this into the general form, we will expand both binomials and rearrange terms.

### Step-by-step solution:

1. Expand the binomials:
   \[
   (x - 11)^2 = x^2 - 22x + 121
   \]
   \[
   (y + 13)^2 = y^2 + 26y + 169
   \]

2. Substituting these expansions back into the equation:
   \[
   x^2 - 22x + 121 + y^2 + 26y + 169 = 25
   \]

3. Combine like terms:
   \[
   x^2 - 22x + y^2 + 26y + 121 + 169 = 25
   \]
   \[
   x^2 - 22x + y^2 + 26y + 290 = 25
   \]

4. Move everything to one side to form the general equation:
   \[
   x^2 - 22x + y^2 + 26y + 290 - 25 = 0
   \]
   \[
   x^2 - 22x + y^2 + 26y + 265 = 0
   \]

This matches the first option in the image.

Thus, the correct answer is:

\[
x^2 - 22x + y^2 + 26y + 265 = 0
\]

Let me know if you need further clarification or details!

### Related Questions:
1. How do you derive the standard form of a circle from the general form?
2. What is the geometric interpretation of the general form of a circle?
3. How can you determine the radius of a circle given its general form?
4. What is the process to find the center of a circle from its equation?
5. How do we convert a quadratic equation in two variables into standard form?

**Tip:** Always check if the constants in your equation match both sides when simplifying!

Express (x - 11)^2 + (y + 13)^2 = 25 in general form.

Learn how to convert the circle equation (x - 11)^2 + (y + 13)^2 = 25 into general form through a step-by-step solution. Explore key algebraic concepts related to circle equations, suitable for Grades 9-11.

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