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The given equation of the sphere is:

\[
(x - 2)^2 + (y - 5)^2 + (z + 6)^2 = 25
\]

This equation is in the standard form of a sphere:

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

where:
- \((h, k, l)\) is the center of the sphere,
- \(r\) is the radius of the sphere.

### Solution
1. By comparing the given equation with the standard form, we can see that:
   - \(h = 2\)
   - \(k = 5\)
   - \(l = -6\)

   Thus, the center of the sphere is \((2, 5, -6)\).

2. The radius \(r\) is the square root of the constant on the right side of the equation:
   \[
   r = \sqrt{25} = 5
   \]

### Answer
- **Center:** \((2, 5, -6)\)
- **Radius:** \(5\)

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:
1. How would the equation change if the center of the sphere was moved to \((0, 0, 0)\)?
2. What is the equation of a sphere with a radius of 10 and a center at \((1, -2, 3)\)?
3. How can you determine if a point lies on the sphere given its equation?
4. How would you find the intersection of this sphere with the xy-plane?
5. If the radius of the sphere doubles, what would be the new equation?

**Tip:** In the equation of a sphere, the value on the right side represents the square of the radius. Always take the square root of this value to find the actual radius.

Find the center and radius of the sphere with equation (x - 2)^2 + (y - 5)^2 + (z + 6)^2 = 25.

Learn how to find the center and radius of the sphere given by the equation (x - 2)^2 + (y - 5)^2 + (z + 6)^2 = 25. This problem demonstrates the use of the standard form of a sphere equation and 3D coordinate geometry. Suitable for high school students in Grades 10-12.

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