Question

Which of the following circles have their centers in the third quadrant? Check all that apply.

Answer 1

B and D

Explanation:

The center of the first one is (-3,6)

The center of the second one is (-9,-12)

The center of the third one is (-14,14)

The center of the fourth one is (-16,-3)

The first one has center in the 2nd

The second one has center in 3rd

The third one has center in the 2nd

The fourth one has center is the 3rd

Answer 2

The correct answer options are B.
`(x + 9)^2 + (y + 12)^2 = 36` and D.
`(x + 16)^2 + ( y + 3)^2 = 17`.

Explanation:

We know that the formula of a circle is
`(x - h)^2 + (y - k)^2 = r^2` where
`k` is the value of the ordinate,
`h` is the value of the abscissa and
`r` is the radius of the circle.

B.
`(x + 9)^2 + (y + 12)^2 = 36`

`[x - (-9)]^2 + [y - (-12)]^2 = 6^2`

Center (-9, -12)

D.
`(x + 16)^2 + ( y + 3)^2 = 17`

`[x - (-16)]^2 + [y - (-3)]^2 =√(17)`

Center (-16, -3)