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 - 2)^2+(y + 1)^2 = 3^2 b. (x + 2)^2+(y - 1)^2 = 3^2 c. (x - 1)^2+(y + 2)^2 = 9 d. (x + 1)^2+(y - 2)^2 = 9

Explanation:

Step1: Recall circle - equation formula

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

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

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

Step3: Substitute values into formula

Substitute $h = 2$, $k=-1$, and $r = 3$ into $(x - h)^2+(y - k)^2=r^2$, we get $(x - 2)^2+(y+1)^2=3^2$.

Answer:

A. $(x - 2)^2+(y + 1)^2=3^2$