Question

question 9 of 10
identify the center and radius of the circle (x + 4)^2+(y - 2)^2 = 16.
a. center: (-4,2), r = 16
b. center: (4,-2), r = 4
c. center: (4,-2), r = 16
d. center: (-4,2), r = 4

Explanation:

Step1: Recall circle - standard form

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

Step2: Identify the center

For the equation $(x + 4)^2+(y - 2)^2=16$, we can rewrite $(x + 4)$ as $(x-(-4))$. So, $a=-4$ and $b = 2$, and the center is $(-4,2)$.

Step3: Identify the radius

Since $r^2=16$, taking the square - root of both sides (and considering the positive value for the radius), we have $r = 4$.

Answer:

D. Center: (-4, 2), r = 4