Question

write an equation of the circle with center (8, - 3) and radius 4.

Explanation:

Step1: Recall the standard - form of a circle equation

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 is $(8,-3)$ and the radius $r = 4$. So, $h = 8$, $k=-3$, and $r = 4$.

Step3: Substitute the values into the equation

Substitute $h = 8$, $k=-3$, and $r = 4$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 8)^2+(y+3)^2 = 16$.

Answer:

$(x - 8)^2+(y + 3)^2=16$