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, C, and E

Explanation:

To solve this, you have to find the two circles with a center on the y-axis.

So let us find the centers of all the circles.

To find the center of a circle you have to look at the h and k values and do the opposite operation of the sign in front. The formula is
`(x-h)^2+(y-k)^2=r^2`.

By applying this rule we can find that the center of the first circle is (0,3), the second circle is (0,5), the third circle is (4,0), the fourth circle's center is at (-6,0) and the last circle is (0,-8).

So after finding the centers we can eliminate two answers, Band D. The reason is those centers are found on the x-axis, but we are looking for the y-axis.

The next step would be to find the equations that have a diameter of 12.

To find the diameter you have to double the radius, so to find how much the radius would have to be you should divide 12 by 2. So the radius would have to be 6.

So based on the formula the radius is squared. So to find an equation that has a radius of 6 you would have to square 6 to get 36. So now we can have our answers of A, C, and E.