What is the standard form of the equation of the circle whose center is at (h, k)?

The standard form of the equation of a circle with center at \((h, k)\) and radius \(r\) is:

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

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

This equation ensures that all points \((x, y)\) on the circle are exactly \(r\) units away from the center.

Would you like more details or have any further questions? 

Here are some related questions:
1. How do you find the radius of a circle given the equation in standard form?
2. How can the equation of a circle be converted from standard form to general form?
3. How do you derive the equation of a circle from the distance formula?
4. What happens to the equation if the center of the circle is at the origin \((0, 0)\)?
5. How do you graph a circle given its equation in standard form?

**Tip:** When dealing with circles, always check if the equation needs to be rewritten in standard form by completing the square!

Learn the standard form of the equation of a circle with center at (h, k) and radius r. This formula, (x - h)^2 + (y - k)^2 = r^2, is fundamental in coordinate geometry and is suitable for students in Grades 9-12.

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