graph and identify the parts of this circle (x-5/2)²+(y-4)²=2

The given equation is:

\[
\left( x - \frac{5}{2} \right)^2 + (y - 4)^2 = 2
\]

This is the equation of a circle in standard form:

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

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

### Identifying the parts:
1. **Center**:
   From the equation, \((h, k)\) represents the center. Here:
   - \(h = \frac{5}{2} = 2.5\)
   - \(k = 4\)

   Therefore, the center of the circle is \((2.5, 4)\).

2. **Radius**:
   The right-hand side of the equation is \(r^2\). Here:
   - \(r^2 = 2\)
   - Therefore, \(r = \sqrt{2}\) (approximately \(1.414\)).

3. **Graph of the circle**:
   - The center is located at \((2.5, 4)\).
   - The radius is \(\sqrt{2}\), so the distance from the center to any point on the circle is approximately \(1.414\) units.

Would you like me to graph this circle for you? Also, feel free to ask any further questions.

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Here are 5 related questions for you to explore:
1. How do you find the equation of a circle given three points on its circumference?
2. What is the significance of completing the square in deriving a circle equation?
3. How do you determine the tangent line to a circle at a given point?
4. How do you find the area of a sector of a circle given the radius and angle?
5. How would you write the equation of a circle if its center is at the origin?

**Tip**: When solving equations involving circles, knowing how to complete the square can be essential for converting general forms into standard forms.

Graph and identify the parts of this circle (x-5/2)²+(y-4)²=2

Learn how to graph and identify the key components of the circle with the equation (x-5/2)²+(y-4)²=2. This guide covers essential geometry concepts including the center, radius, and standard form of a circle equation. Suitable for students in Grades 9-10.

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