Question

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36

Answer 1

Answer: The correct options are:

x^2 + (y - 6)^2 = 36 (center at (0, 6))

x^2 + (y + 6)^2 = 36 (center at (0, -6))

Explanation:

Both equations have the form (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Since the center lies on the y-axis, the x-coordinate is 0. The diameter is 12 units, so the radius is 6 units, and the equation becomes x^2 + (y - k)^2 = 36. For the center to be on the y-axis, the y-coordinate of the center must be either positive or negative 6. Therefore, the correct options are (0,6) and (0,-6).