Review the graph of circle A.

Which equation represents circle A?

(*x* – 2)2 + *y*2 = 5

(*x* + 2)2 + *y*2 = 5

(*x* – 2)2 + *y*2 = 25

(*x* + 2)2 + *y*2 = 25

The general equation of a circle is given by:

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

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

Given the four possible equations, let's break them down:

1. **\((x - 2)^2 + y^2 = 5\)**: This represents a circle with center at \((2, 0)\) and radius \(\sqrt{5}\).
   
2. **\((x + 2)^2 + y^2 = 5\)**: This represents a circle with center at \((-2, 0)\) and radius \(\sqrt{5}\).

3. **\((x - 2)^2 + y^2 = 25\)**: This represents a circle with center at \((2, 0)\) and radius \(5\).

4. **\((x + 2)^2 + y^2 = 25\)**: This represents a circle with center at \((-2, 0)\) and radius \(5\).

### Key Points to Determine the Correct Equation:
- **Center**: Look at the values for \(h\) and \(k\). The equations have centers at either \((2, 0)\) or \((-2, 0)\).
- **Radius**: The radius is either \(\sqrt{5}\) (if the equation has 5 on the right side) or \(5\) (if the equation has 25 on the right side).

Based on the graph of circle \(A\), you would need to identify:
1. The center of the circle (which will be either \((2, 0)\) or \((-2, 0)\)).
2. The radius (which will help distinguish between the circles with radii \(\sqrt{5}\) and \(5\)).

If the center of the circle is \((2, 0)\) and the radius is \(5\), then the correct equation is:

\[
(x - 2)^2 + y^2 = 25
\]

If the center is \((-2, 0)\) and the radius is \(5\), then the correct equation is:

\[
(x + 2)^2 + y^2 = 25
\]

Would you like more details or have any questions?

Here are 5 relative questions to consider:
1. How do you find the center of a circle from its equation?
2. What does the number on the right side of the equation of a circle represent?
3. How can you determine the radius of a circle if you know the equation?
4. What happens to the graph of a circle if you change the center coordinates?
5. How does changing the radius affect the size of the circle on the coordinate plane?

**Tip:** Always square the radius to match it with the value on the right side of the circle's equation.

Explore how to identify the equation of circle A based on its graph analysis. Understand the components such as center coordinates and radius to determine the correct circle equation. Suitable for high school students studying geometry.

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