(x-5)² + (y-4.5)² = 1 what is the circle and radius

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

For the equation:
\[
(x - 5)^2 + (y - 4.5)^2 = 1
\]
- The center of the circle \((h, k)\) is \((5, 4.5)\).
- The radius \(r\) is \(\sqrt{1} = 1\).

### Answer:
- **Center**: \((5, 4.5)\)
- **Radius**: \(1\)

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the equation of a circle with center \((2, -3)\) and radius 4?
2. How do you find the area of a circle if the radius is known?
3. How does the general form of a circle equation differ from the standard form?
4. If a point lies on this circle, what is the distance from the point to the center?
5. What happens to the equation of a circle if the radius doubles?

**Tip:** The radius is always positive and represents the distance from the center to any point on the circle.

Understand how to find the center and radius of a circle from the equation (x-5)² + (y-4.5)² = 1. This geometry problem explores key concepts like the standard equation of a circle and involves simple algebra. Suitable for students in Grades 9-10.

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