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The value of \( k \) is \( 6 \), which corresponds to option B.

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Here are five related questions to expand on this concept:
1. How do you complete the square for a quadratic expression?
2. How do you find the radius of a circle given its equation?
3. What are the steps to identify the center of a circle from its general equation?
4. How would the equation change if the circle were translated?
5. How can you apply the method of completing the square to solve different types of equations?

**Tip:** Completing the square is a powerful method to transform quadratic equations into a form that is easy to interpret, especially when dealing with conic sections like circles.

An equation of a circle in the xy-plane is shown: x^2 - 18x + y^2 - 12y = -17. If the center of the circle is (9, k), where k is a constant, what is the value of k?

Learn how to find the value of k in the general equation of a circle, x^2 - 18x + y^2 - 12y = -17. This problem involves completing the square and applying the standard equation of a circle. Suitable for students in Grades 9-11.

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