Question

question 8 of 10 which of the following circles have their centers in the second quadrant? check all that apply. a. (x + 3)^2+(y - 2)^2 = 8 b. (x - 2)^2+(y + 7)^2 = 64 c. (x - 5)^2+(y + 5)^2 = 9 d. (x + 12)^2+(y - 9)^2 = 19

Explanation:

Step1: Recall circle - center formula

The standard form of a circle is $(x - a)^2+(y - b)^2 = r^2$, and its center is at the point $(a,b)$.

Step2: Find centers of each circle

For circle A: $(x + 3)^2+(y - 2)^2 = 8$, the center is $(-3,2)$.
For circle B: $(x - 2)^2+(y + 7)^2 = 64$, the center is $(2, - 7)$.
For circle C: $(x - 5)^2+(y + 5)^2 = 9$, the center is $(5,-5)$.
For circle D: $(x + 12)^2+(y - 9)^2 = 19$, the center is $(-12,9)$.

Step3: Determine quadrant of centers

In the second - quadrant, $x\lt0$ and $y\gt0$. The center $(-3,2)$ and $(-12,9)$ satisfy this condition.

Answer:

A. $(x + 3)^2+(y - 2)^2 = 8$, D. $(x + 12)^2+(y - 9)^2 = 19$