https://file.aiquickdraw.com/mathbot/file/1726645085759y734yav6.jpg

The equation shown in the image is:

\[
(x - 3)^2 + (y + 5)^2 = 4
\]

This is the equation of a circle in standard form:

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

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

In your equation:
- \(h = 3\) (since \((x - 3)\)) 
- \(k = -5\) (since \((y + 5)\) can be written as \((y - (-5))\)).

So, the center of the circle is at \((3, -5)\).

Would you like more details on how this equation works, or do you have other questions?

Here are 5 related questions to expand on this topic:
1. How do you find the radius of the circle from the given equation?
2. What changes would shift the center of the circle to the origin \((0, 0)\)?
3. How can you determine the diameter of the circle?
4. How do the values of \(h\) and \(k\) affect the position of the circle?
5. How would you rewrite this equation if the radius were doubled?

**Tip:** The number under the squared terms represents the radius squared. So, for your circle, the radius is \( \sqrt{4} = 2 \).

The graph of (x - 3)^2 + (y + 5)^2 = 4 has center with coordinates ____ (Type an ordered pair).

Learn how to find the center of a circle from the equation (x - 3)^2 + (y + 5)^2 = 4. This example covers key geometry concepts related to the equation of a circle. Suitable for students in Grades 9-12.

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