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This image provides an overview of the standard equation of a circle. Here's a breakdown:

1. **Standard Equation of a Circle**: The equation for a circle with a center \((h, k)\) and radius \(r\) is:
   \[
   (x - h)^2 + (y - k)^2 = r^2
   \]
   - \( (h, k) \) represents the coordinates of the circle's center.
   - \( r \) is the radius of the circle.

2. **Special Case - Circle at the Origin**: When the circle's center is at the origin \((0, 0)\), the equation simplifies to:
   \[
   x^2 + y^2 = r^2
   \]
   This version is used when \(h\) and \(k\) are both zero.

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### Related Questions
1. How do you derive the equation of a circle given three points on the circle?
2. What changes occur in the equation if the circle is translated horizontally or vertically?
3. How would you find the radius of a circle given the center and a point on the circle?
4. Can the equation of a circle be expressed in polar coordinates?
5. How do you convert the general form of a circle's equation to its standard form?

### Tip:
To identify the radius of a circle from the equation \((x - h)^2 + (y - k)^2 = r^2\), take the square root of the right side.

Explore the standard equation of a circle with center (h, k) and radius r. Learn to identify and graph circles using the equation (x - h)^2 + (y - k)^2 = r^2, and understand special cases like circles centered at the origin.

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