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

The given equation is of the form \((x - h)^2 + (y - k)^2 = r^2\), which represents the equation of a circle. 

- The center of the circle is at \((h, k)\), and
- The radius \(r\) is the square root of the number on the right-hand side.

From your equation \((x - 5)^2 + (y - 4.5)^2 = 1\):
- The center is \((5, 4.5)\),
- The radius \(r = \sqrt{1} = 1\).

The formula for the area \(A\) of a circle is:

\[
A = \pi r^2
\]

Substitute \(r = 1\):

\[
A = \pi (1)^2 = \pi
\]

Thus, the area of the circle is \(\pi\), which is approximately \(3.1416\).

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the circumference of this circle?
2. How do you find the equation of a circle given its center and radius?
3. How would the area change if the radius were doubled?
4. What is the distance from the origin to the center of this circle?
5. How can you find the equation of a tangent line to this circle at a given point?

**Tip**: Always remember the general form of a circle equation to easily identify the center and radius!

Learn how to find the area of a circle from the equation (x - 5)² + (y - 4.5)² = 1. This problem explores the geometry of circles, covering the equation of a circle and the formula for calculating the area. Suitable for students in Grades 8-10.

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