Answer:
x2 + (y + 8)2 = 36
x2 + (y – 5)2 = 6
Explanation:
If the center of a circle lies on the y-axis, the x-coordinate of the center is 0. Also, the diameter of the circle is 12 units, so the radius of the circle is 6 units.
Using these facts, we can eliminate some of the options:
x2 + (y – 3)2 = 36 : This equation represents a circle with center at (0, 3) and radius 6, so it does not have its center on the y-axis.
(x – 4)² + y² = 36 : This equation represents a circle with center at (4, 0) and radius 6, so it does not have its center on the y-axis.
(x + 6)² + y² = 144 : This equation represents a circle with center at (-6, 0) and radius 12, so it does not have its center on the y-axis.
Therefore, the remaining options are:
x2 + (y + 8)2 = 36 : This equation represents a circle with center at (0, -8) and radius 6, which has its center on the y-axis.
x2 + (y – 5)2 = 6 : This equation represents a circle with center at (0, 5) and radius sqrt(6), which has its center on the y-axis.
So the two equations that represent circles with a diameter of 12 units and a center that lies on the y-axis are:
x2 + (y + 8)2 = 36
x2 + (y – 5)2 = 6