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

(x - 6)² + y² = 36 and x2 + (y + 6)2 = 36.

Explanation:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)² + (y - k)² = r².

So, for a circle with a diameter of 12 units, the radius is 6 units.

For the center of the circle to lie on the y-axis, the x-coordinate, h, is 0.

So, the equation for a circle with center (0, k) and radius 6 units is:

(x - 0)² + (y - k)² = 6²

x² + (y - k)² = 36

Two possible values for the y-coordinate of the center, k, that would give us two different circles are k = 6 and k = -6.

So, the two equations are:

x² + (y - 6)² = 36

and

x² + (y + 6)² = 36.