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

x^2 + (y - 3) ^2 = 36

Step-by-step explanation:

The standard equation of a circle with center at (h, k) and radius r is

(x - h) ^2 + (y - k) ^2 = r^2.

If the center lies on the y-axis, then h = 0: (x - 0) ^2 + (y - k) ^2 = r^2

If the circle diameter is 12, then the circle radius is 6, and so r^2 = 36

So, among the given equations, your

x^2 + (y - 3) ^2 = 36 is correct (but only if you use " ^ " for exponentiation).

A & E

x2 + (y - 3) 2 = 36

x2 + (y + 8) 2 = 36