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To write the standard equation of the circle shown in the graph, we need two key pieces of information:

1. **The center of the circle** (denoted as point \( P \)).
2. **The radius of the circle**.

### Step 1: Identify the center of the circle
From the graph, the center \( P \) is located at the coordinates \( (-2, 5) \).

### Step 2: Identify the radius of the circle
To find the radius, we observe the distance from the center to any point on the circumference. The circle seems to pass through the point \( (-2, 8) \), which is directly above the center. The distance from \( (-2, 5) \) to \( (-2, 8) \) is:
\[
8 - 5 = 3
\]
So, the radius \( r = 3 \).

### Step 3: Write the equation of the circle
The standard form of the equation of a circle with center \( (h, k) \) and radius \( r \) is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Substituting \( h = -2 \), \( k = 5 \), and \( r = 3 \):
\[
(x + 2)^2 + (y - 5)^2 = 9
\]

Thus, the standard equation of the circle is:
\[
(x + 2)^2 + (y - 5)^2 = 9
\]

Would you like further explanation on any part of this? 

Here are some related questions:
1. What is the general formula for a circle and how can it be derived?
2. How do you find the radius if you're given two points on a circle?
3. Can a circle's radius be a negative value?
4. What happens to the equation if the circle is centered at the origin?
5. How do you convert an equation of a circle from general form to standard form?

**Tip:** Always ensure to accurately determine the coordinates of the center and the radius before writing the equation of a circle.

Write the standard equation of circle P shown in the graph.

Find the standard equation of a circle with center (-2, 5) and radius 3, applying the formula (x - h)^2 + (y - k)^2 = r^2. This geometry problem demonstrates how to derive the equation from a graph.

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