https://file.aiquickdraw.com/mathbot/file/1729222422447ac6gy5so.jpg

The problem in the image asks to write the equation of a circle in standard form given the center \((-5, -1)\) and radius \(2\).

The standard form of the equation of a circle is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.

Here:
- \(h = -5\),
- \(k = -1\),
- \(r = 2\).

Substitute these values into the standard form:
\[
(x - (-5))^2 + (y - (-1))^2 = 2^2
\]
which simplifies to:
\[
(x + 5)^2 + (y + 1)^2 = 4
\]

This is the equation of the circle in standard form.

Would you like more details about how to graph the circle or any specific part of the process?

### Related Questions:
1. What is the general form of a circle's equation, and how is it derived from the standard form?
2. How do transformations of the center affect the graph of a circle?
3. What are the differences between the standard and general form of a circle’s equation?
4. Can the equation of a circle be derived from three given points? If so, how?
5. How would the equation change if the radius were doubled?

### Tip:
Always double-check whether the equation is simplified fully, especially when working with negatives in the center coordinates!

Given a circle with center (-5, -1) and radius 2, write an equation of the circle in standard form and graph the circle.

Learn how to write the equation of a circle with a center at (-5, -1) and a radius of 2. This example demonstrates the application of the standard form of a circle's equation, suitable for students in Grades 9-10.

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