Question

question 3 of 10 the circle below is centered at the point (4, -3) and has a radius of length 3. what is its equation? a. (x - 4)^2+(y + 3)^2 = 3^2 b. (x + 4)^2+(y - 3)^2 = 3^2 c. (x - 3)^2+(y - 4)^2 = 9 d. (x - 3)^2+(y + 4)^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 the values of $h$, $k$, and $r$

Given that the center is $(4,-3)$ and the radius $r = 3$. So $h = 4$, $k=-3$, and $r = 3$.

Step3: Substitute the values into the formula

Substitute $h = 4$, $k=-3$, and $r = 3$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 4)^2+(y-(-3))^2=3^2$, which simplifies to $(x - 4)^2+(y + 3)^2=3^2$.

Answer:

A. $(x - 4)^2+(y + 3)^2=3^2$