The value of $k$ is $6$, which corresponds to option B.

Would you like more details or have any other questions?

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.