Question

question 10 of 10 the circle below is centered at the point (3, 1) and has a radius of length 2. what is its equation? a. (x - 1)^2+(y - 3)^2 = 4 b. (x + 3)^2+(y + 1)^2 = 4 c. (x + 1)^2+(y + 3)^2 = 2 d. (x - 3)^2+(y - 1)^2 = 2^2

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 $(3,1)$ and the radius $r = 2$. So $h = 3$, $k = 1$, and $r=2$.

Step3: Substitute values into formula

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

Answer:

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