The given equation seems to define a circle with:

- **Center**: \( P(1, -3) \)
- **Radius**: \( r = 4 \)

The general equation of a circle is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
Where \( (h, k) \) is the center of the circle and \( r \) is the radius.

Using your provided values:
- \( h = 1 \)
- \( k = -3 \)
- \( r = 4 \)

The equation becomes:
\[
(x - 1)^2 + (y + 3)^2 = 16
\]

This is the equation of a circle with center \( (1, -3) \) and radius \( 4 \).

Would you like any details or further explanation?

Here are 5 related questions:
1. How do you find the center and radius of a circle from its equation?
2. What is the standard form of a circle's equation?
3. Can you graph the circle from the equation provided?
4. How do you convert a circle's general equation into its standard form?
5. What are the real-world applications of circle equations?

**Tip**: To find the distance between two points, use the distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).

Explore the detailed solution for finding the equation of a circle with center (1, -3) and radius 4. This problem covers the key geometry concepts of circle equations, suitable for students in Grades 9-12.

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