Final answer:
The equation represents a circle with center (0,3) and radius √7, thus none of the given options are correct.
Step-by-step explanation:
To show that the equation x² + y² - 6y + 2 = 0 represents a circle, we need to complete the square for the y-terms. First, we rewrite the equation as:
x² + (y² - 6y) = -2.
Next, we add ³9 to both sides to complete the square, which gives us:
x² + (y - 3)² = -2 + 9,
which simplifies to:
x² + (y - 3)² = 7.
This equation is in the standard form for a circle (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. Comparing this to our equation, the center of the circle is (0,3) and the radius is √7.
Therefore, the given options are all incorrect as the correct center and radius are not listed among them.