Question

question 2 of 10 the circle below is centered at the point (-2, 1) and has a radius of length 3. what is its equation? a. (x + 1)^2+(y - 2)^2 = 9 b. (x - 1)^2+(y + 2)^2 = 3 c. (x - 2)^2+(y + 1)^2 = 3 d. (x + 2)^2+(y - 1)^2 = 9

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the values of $h$, $k$, and $r$

Given that the center of the circle is $(-2,1)$, so $h=-2$ and $k = 1$. The radius $r = 3$.

Step3: Substitute the values into the formula

Substitute $h=-2$, $k = 1$, and $r = 3$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-2))^2+(y - 1)^2=3^2$, which simplifies to $(x + 2)^2+(y - 1)^2=9$.

Answer:

D. $(x + 2)^2+(y - 1)^2=9$