Question

find the standard form of the equation for the circle with the following properties. center (6, - 7) and radius 6

Explanation:

Step1: Recall circle - equation formula

The standard - form 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 values of $h$, $k$, and $r$

Given that the center is $(6,-7)$ and the radius $r = 6$. So, $h = 6$, $k=-7$, and $r = 6$.

Step3: Substitute values into the formula

Substitute $h = 6$, $k=-7$, and $r = 6$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 6)^2+(y+7)^2=36$.

Answer:

$(x - 6)^2+(y + 7)^2=36$