(x-5)² + (y-4.5)² = 1  what is the area

The given equation \((x - 5)^2 + (y - 4.5)^2 = 1\) is the equation of a circle. Here's how we analyze it:

### General Form of a Circle's Equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.

### From the given equation:
- The center is \((5, 4.5)\).
- The radius \(r = 1\) (since \(r^2 = 1\)).

### Area of a Circle:
The area \(A\) of a circle is given by:
\[
A = \pi r^2
\]
Substituting \(r = 1\):
\[
A = \pi \times 1^2 = \pi
\]
Thus, the area of the circle is \(\pi\) square units.

Would you like further details or have any other questions?

### Related Questions:
1. What is the circumference of the circle?
2. How would the equation change if the radius was doubled?
3. What is the distance from the origin to the center of the circle?
4. How does the area change if the equation is \((x-5)^2 + (y-4.5)^2 = 4\)?
5. What are the x- and y-intercepts of the circle?

**Tip:** The radius in the equation of a circle is always the square root of the constant on the right-hand side.

Solve the equation of a circle (x-5)² + (y-4.5)² = 1 to find the area of the circle. Learn about the equation of a circle and how to use it to determine the area using the formula A = πr². Suitable for Grades 8-10.

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