https://file.aiquickdraw.com/mathbot/file/1729004612896bdyaxhbs.jpg

Let's analyze the equation given in the image:

\[
(x - 1)^2 + (y + 5)^2 = 4
\]

This is the equation of a circle in standard form:

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

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

From the given equation, we can identify:
- \(h = 1\) (since \(x - 1\))
- \(k = -5\) (since \(y + 5\) is equivalent to \(y - (-5)\))
- \(r^2 = 4\), so \(r = 2\)

### Therefore:
- The **center** of the circle is \((1, -5)\).
- The **radius** of the circle is \(2\).

#### Would you like to know how to graph it or need further details?

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### 5 Questions for Further Exploration:
1. How do you find the radius if the right side of the equation was different?
2. How would you find the equation if the radius and center were given?
3. What changes in the equation when the circle is centered at the origin?
4. How do you convert a general equation of a circle into the standard form?
5. How would the graph of this circle change if the radius were doubled?

### Tip:
Always check if the equation is in standard form, as it makes identifying the center and radius of the circle much easier!

Find the center and radius of the circle with the given equation: (x - 1)^2 + (y + 5)^2 = 4

Learn how to find the center and radius of a circle given the equation (x - 1)^2 + (y + 5)^2 = 4. This geometry problem explains the standard form of a circle equation and walks you through the solution step by step. Suitable for students in Grades 9-11.

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