, correctly represents a circle with a radius of 2√6. Other options depict an ellipse or circles with different radii. Option D is the correct choice.
The correct choice is D, represented by the equation which describes a circle. Step by step:
1. The given equation:

2. Divide both sides by 6 to simplify:

3. Compare this with the general form of a circle equation:
where r is the radius.
4. Conclude that the circle has a radius of

5. Therefore, the equation
indeed represents a circle with a radius of
.
6. Eliminate other options: A (ellipse), B (circle with radius 5), and C (circle with radius 4) don't match the given equation.
In summary, option D correctly represents a circle with a radius of
