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

A) x² + (y - 3)² = 36

E) x² + (y + 8)² = 36

Explanation:

The formula for the equation of a circle is:

`\boxed{(x-h)^2+(y-k)^2=r^2}`

where:

• (h, k) is the center of the circle.
• r is the radius of the circle.

The diameter of a circle is twice its radius.

Therefore, if the diameter of the circle is 12 units, its radius is r = 6.

If the center of the circle lies on the y-axis, the x-value of the center is zero. Therefore, h = 0.

Substituting this information into the formula for the equation of the circle gives:

`(x-0)^2+(y-h)^2=6^2`

`x^2+(y-h)^2=36`

Therefore, the two equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

• x² + (y - 3)² = 36

• x² + (y + 8)² = 36