Question

find an equation of a circle that satisfies the given conditions.
center (9, -7), radius 4

Explanation:

Step1: Recall circle standard form

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

Step2: Substitute given values

Substitute $h=9$, $k=-7$, $r=4$ into the formula:
$(x-9)^2+(y-(-7))^2=4^2$

Step3: Simplify the equation

Simplify the signs and the radius squared:
$(x-9)^2+(y+7)^2=16$

Answer:

$(x-9)^2+(y+7)^2=16$